diff --git a/packages/eslint-plugin/docs/rules/no-explicit-any.md b/packages/eslint-plugin/docs/rules/no-explicit-any.md
index 0c271392349..c440d3bdc60 100644
--- a/packages/eslint-plugin/docs/rules/no-explicit-any.md
+++ b/packages/eslint-plugin/docs/rules/no-explicit-any.md
@@ -119,30 +119,23 @@ function foo2(...args: readonly any[]): void {}
 function foo3(...args: Array<any>): void {}
 function foo4(...args: ReadonlyArray<any>): void {}
 
-const bar1 = (...args: any[]): void {}
-const bar2 = (...args: readonly any[]): void {}
-const bar3 = (...args: Array<any>): void {}
-const bar4 = (...args: ReadonlyArray<any>): void {}
+declare function bar(...args: any[]): void;
 
-const baz1 = function (...args: any[]) {}
-const baz2 = function (...args: readonly any[]) {}
-const baz3 = function (...args: Array<any>) {}
-const baz4 = function (...args: ReadonlyArray<any>) {}
+const baz = (...args: any[]) => {};
+const qux = function(...args: any[]) {};
 
-interface Qux1 { (...args: any[]): void; }
-interface Qux2 { (...args: readonly any[]): void; }
-interface Qux3 { (...args: Array<any>): void; }
-interface Qux4 { (...args: ReadonlyArray<any>): void; }
+type Quux = (...args: any[]) => void;
+type Quuz = new (...args: any[]) => void;
 
-function quux1(fn: (...args: any[]) => void): void {}
-function quux2(fn: (...args: readonly any[]) => void): void {}
-function quux3(fn: (...args: Array<any>) => void): void {}
-function quux4(fn: (...args: ReadonlyArray<any>) => void): void {}
-
-function quuz1(): ((...args: any[]) => void) {}
-function quuz2(): ((...args: readonly any[]) => void) {}
-function quuz3(): ((...args: Array<any>) => void) {}
-function quuz4(): ((...args: ReadonlyArray<any>) => void) {}
+interface Grault {
+  (...args: any[]): void;
+}
+interface Corge {
+  new (...args: any[]): void;
+}
+interface Garply {
+  f(...args: any[]): void;
+}
 ```
 
 Examples of **correct** code for the `{ "ignoreRestArgs": true }` option:
@@ -155,30 +148,23 @@ function foo2(...args: readonly any[]): void {}
 function foo3(...args: Array<any>): void {}
 function foo4(...args: ReadonlyArray<any>): void {}
 
-const bar1 = (...args: any[]): void {}
-const bar2 = (...args: readonly any[]): void {}
-const bar3 = (...args: Array<any>): void {}
-const bar4 = (...args: ReadonlyArray<any>): void {}
-
-const baz1 = function (...args: any[]) {}
-const baz2 = function (...args: readonly any[]) {}
-const baz3 = function (...args: Array<any>) {}
-const baz4 = function (...args: ReadonlyArray<any>) {}
-
-interface Qux1 { (...args: any[]): void; }
-interface Qux2 { (...args: readonly any[]): void; }
-interface Qux3 { (...args: Array<any>): void; }
-interface Qux4 { (...args: ReadonlyArray<any>): void; }
-
-function quux1(fn: (...args: any[]) => void): void {}
-function quux2(fn: (...args: readonly any[]) => void): void {}
-function quux3(fn: (...args: Array<any>) => void): void {}
-function quux4(fn: (...args: ReadonlyArray<any>) => void): void {}
-
-function quuz1(): ((...args: any[]) => void) {}
-function quuz2(): ((...args: readonly any[]) => void) {}
-function quuz3(): ((...args: Array<any>) => void) {}
-function quuz4(): ((...args: ReadonlyArray<any>) => void) {}
+declare function bar(...args: any[]): void;
+
+const baz = (...args: any[]) => {};
+const qux = function(...args: any[]) {};
+
+type Quux = (...args: any[]) => void;
+type Quuz = new (...args: any[]) => void;
+
+interface Grault {
+  (...args: any[]): void;
+}
+interface Corge {
+  new (...args: any[]): void;
+}
+interface Garply {
+  f(...args: any[]): void;
+}
 ```
 
 ## When Not To Use It
diff --git a/packages/eslint-plugin/src/rules/no-explicit-any.ts b/packages/eslint-plugin/src/rules/no-explicit-any.ts
index 91765c40e26..795dae01725 100644
--- a/packages/eslint-plugin/src/rules/no-explicit-any.ts
+++ b/packages/eslint-plugin/src/rules/no-explicit-any.ts
@@ -53,18 +53,23 @@ export default util.createRule<Options, MessageIds>({
   ],
   create(context, [{ ignoreRestArgs, fixToUnknown }]) {
     /**
-     * Checks if the node is an arrow function, function declaration or function expression
+     * Checks if the node is an arrow function, function/constructor declaration or function expression
      * @param node the node to be validated.
-     * @returns true if the node is an arrow function, function declaration, function expression, function type, or call signature
+     * @returns true if the node is any kind of function declaration or expression
      * @private
      */
     function isNodeValidFunction(node: TSESTree.Node): boolean {
       return [
-        AST_NODE_TYPES.ArrowFunctionExpression,
-        AST_NODE_TYPES.FunctionDeclaration,
-        AST_NODE_TYPES.FunctionExpression,
-        AST_NODE_TYPES.TSFunctionType,
-        AST_NODE_TYPES.TSCallSignatureDeclaration,
+        AST_NODE_TYPES.ArrowFunctionExpression, // const x = (...args: any[]) => {};
+        AST_NODE_TYPES.FunctionDeclaration, // function f(...args: any[]) {}
+        AST_NODE_TYPES.FunctionExpression, // const x = function(...args: any[]) {};
+        AST_NODE_TYPES.TSEmptyBodyFunctionExpression, // declare class A { f(...args: any[]): unknown; }
+        AST_NODE_TYPES.TSFunctionType, // type T = (...args: any[]) => unknown;
+        AST_NODE_TYPES.TSConstructorType, // type T = new (...args: any[]) => unknown
+        AST_NODE_TYPES.TSCallSignatureDeclaration, // type T = {(...args: any[]): unknown};
+        AST_NODE_TYPES.TSConstructSignatureDeclaration, // type T = {new (...args: any[]): unknown};
+        AST_NODE_TYPES.TSMethodSignature, // type T = {f(...args: any[]): unknown};
+        AST_NODE_TYPES.TSDeclareFunction, // declare function _8(...args: any[]): unknown;
       ].includes(node.type);
     }
 
diff --git a/packages/eslint-plugin/tests/rules/no-explicit-any.test.ts b/packages/eslint-plugin/tests/rules/no-explicit-any.test.ts
index dde8b938175..1a5b9c5778c 100644
--- a/packages/eslint-plugin/tests/rules/no-explicit-any.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-explicit-any.test.ts
@@ -255,6 +255,118 @@ interface Qux4 {
       code: 'function quuz4(): (...args: ReadonlyArray<any>) => void {}',
       options: [{ ignoreRestArgs: true }],
     },
+    {
+      code: 'type Fred1 = (...args: any[]) => void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'type Fred2 = (...args: readonly any[]) => void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'type Fred3 = (...args: Array<any>) => void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'type Fred4 = (...args: ReadonlyArray<any>) => void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'type Corge1 = new (...args: any[]) => void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'type Corge2 = new (...args: readonly any[]) => void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'type Corge3 = new (...args: Array<any>) => void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'type Corge4 = new (...args: ReadonlyArray<any>) => void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: `
+interface Grault1 {
+  new (...args: any[]): void;
+}
+      `,
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: `
+interface Grault2 {
+  new (...args: readonly any[]): void;
+}
+      `,
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: `
+interface Grault3 {
+  new (...args: Array<any>): void;
+}
+      `,
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: `
+interface Grault4 {
+  new (...args: ReadonlyArray<any>): void;
+}
+      `,
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: `
+interface Garply1 {
+  f(...args: any[]): void;
+}
+      `,
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: `
+interface Garply2 {
+  f(...args: readonly any[]): void;
+}
+      `,
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: `
+interface Garply3 {
+  f(...args: Array<any>): void;
+}
+      `,
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: `
+interface Garply4 {
+  f(...args: ReadonlyArray<any>): void;
+}
+      `,
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'declare function waldo1(...args: any[]): void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'declare function waldo2(...args: readonly any[]): void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'declare function waldo3(...args: Array<any>): void;',
+      options: [{ ignoreRestArgs: true }],
+    },
+    {
+      code: 'declare function waldo4(...args: ReadonlyArray<any>): void;',
+      options: [{ ignoreRestArgs: true }],
+    },
   ],
   invalid: ([
     {
@@ -737,7 +849,7 @@ type obj = {
       ],
     },
     {
-      code: `class Foo<t = any> extends Bar<any> {}`,
+      code: 'class Foo<t = any> extends Bar<any> {}',
       errors: [
         {
           messageId: 'unexpectedAny',
@@ -746,11 +858,11 @@ type obj = {
           suggestions: [
             {
               messageId: 'suggestUnknown',
-              output: `class Foo<t = unknown> extends Bar<any> {}`,
+              output: 'class Foo<t = unknown> extends Bar<any> {}',
             },
             {
               messageId: 'suggestNever',
-              output: `class Foo<t = never> extends Bar<any> {}`,
+              output: 'class Foo<t = never> extends Bar<any> {}',
             },
           ],
         },
@@ -761,18 +873,18 @@ type obj = {
           suggestions: [
             {
               messageId: 'suggestUnknown',
-              output: `class Foo<t = any> extends Bar<unknown> {}`,
+              output: 'class Foo<t = any> extends Bar<unknown> {}',
             },
             {
               messageId: 'suggestNever',
-              output: `class Foo<t = any> extends Bar<never> {}`,
+              output: 'class Foo<t = any> extends Bar<never> {}',
             },
           ],
         },
       ],
     },
     {
-      code: `abstract class Foo<t = any> extends Bar<any> {}`,
+      code: 'abstract class Foo<t = any> extends Bar<any> {}',
       errors: [
         {
           messageId: 'unexpectedAny',
@@ -781,11 +893,11 @@ type obj = {
           suggestions: [
             {
               messageId: 'suggestUnknown',
-              output: `abstract class Foo<t = unknown> extends Bar<any> {}`,
+              output: 'abstract class Foo<t = unknown> extends Bar<any> {}',
             },
             {
               messageId: 'suggestNever',
-              output: `abstract class Foo<t = never> extends Bar<any> {}`,
+              output: 'abstract class Foo<t = never> extends Bar<any> {}',
             },
           ],
         },
@@ -796,18 +908,18 @@ type obj = {
           suggestions: [
             {
               messageId: 'suggestUnknown',
-              output: `abstract class Foo<t = any> extends Bar<unknown> {}`,
+              output: 'abstract class Foo<t = any> extends Bar<unknown> {}',
             },
             {
               messageId: 'suggestNever',
-              output: `abstract class Foo<t = any> extends Bar<never> {}`,
+              output: 'abstract class Foo<t = any> extends Bar<never> {}',
             },
           ],
         },
       ],
     },
     {
-      code: `abstract class Foo<t = any> implements Bar<any>, Baz<any> {}`,
+      code: 'abstract class Foo<t = any> implements Bar<any>, Baz<any> {}',
       errors: [
         {
           messageId: 'unexpectedAny',
@@ -816,11 +928,13 @@ type obj = {
           suggestions: [
             {
               messageId: 'suggestUnknown',
-              output: `abstract class Foo<t = unknown> implements Bar<any>, Baz<any> {}`,
+              output:
+                'abstract class Foo<t = unknown> implements Bar<any>, Baz<any> {}',
             },
             {
               messageId: 'suggestNever',
-              output: `abstract class Foo<t = never> implements Bar<any>, Baz<any> {}`,
+              output:
+                'abstract class Foo<t = never> implements Bar<any>, Baz<any> {}',
             },
           ],
         },
@@ -831,11 +945,13 @@ type obj = {
           suggestions: [
             {
               messageId: 'suggestUnknown',
-              output: `abstract class Foo<t = any> implements Bar<unknown>, Baz<any> {}`,
+              output:
+                'abstract class Foo<t = any> implements Bar<unknown>, Baz<any> {}',
             },
             {
               messageId: 'suggestNever',
-              output: `abstract class Foo<t = any> implements Bar<never>, Baz<any> {}`,
+              output:
+                'abstract class Foo<t = any> implements Bar<never>, Baz<any> {}',
             },
           ],
         },
@@ -846,18 +962,20 @@ type obj = {
           suggestions: [
             {
               messageId: 'suggestUnknown',
-              output: `abstract class Foo<t = any> implements Bar<any>, Baz<unknown> {}`,
+              output:
+                'abstract class Foo<t = any> implements Bar<any>, Baz<unknown> {}',
             },
             {
               messageId: 'suggestNever',
-              output: `abstract class Foo<t = any> implements Bar<any>, Baz<never> {}`,
+              output:
+                'abstract class Foo<t = any> implements Bar<any>, Baz<never> {}',
             },
           ],
         },
       ],
     },
     {
-      code: `new Foo<any>()`,
+      code: 'new Foo<any>()',
       errors: [
         {
           messageId: 'unexpectedAny',
@@ -867,7 +985,7 @@ type obj = {
       ],
     },
     {
-      code: `Foo<any>()`,
+      code: 'Foo<any>()',
       errors: [
         {
           messageId: 'unexpectedAny',
@@ -943,7 +1061,7 @@ const test = <T extends Partial<never>>() => {};
       ],
     },
     {
-      code: `type Any = any;`,
+      code: 'type Any = any;',
       options: [{ ignoreRestArgs: true }],
       errors: [
         {
@@ -954,7 +1072,7 @@ const test = <T extends Partial<never>>() => {};
       ],
     },
     {
-      code: `function foo5(...args: any) {}`,
+      code: 'function foo5(...args: any) {}',
       options: [{ ignoreRestArgs: true }],
       errors: [
         {
@@ -965,7 +1083,7 @@ const test = <T extends Partial<never>>() => {};
       ],
     },
     {
-      code: `const bar5 = function (...args: any) {}`,
+      code: 'const bar5 = function (...args: any) {}',
       options: [{ ignoreRestArgs: true }],
       errors: [
         {
@@ -976,7 +1094,7 @@ const test = <T extends Partial<never>>() => {};
       ],
     },
     {
-      code: `const baz5 = (...args: any) => {}`,
+      code: 'const baz5 = (...args: any) => {}',
       options: [{ ignoreRestArgs: true }],
       errors: [
         {
@@ -987,7 +1105,7 @@ const test = <T extends Partial<never>>() => {};
       ],
     },
     {
-      code: `interface Qux5 { (...args: any): void; }`,
+      code: 'interface Qux5 { (...args: any): void; }',
       options: [{ ignoreRestArgs: true }],
       errors: [
         {
@@ -998,7 +1116,7 @@ const test = <T extends Partial<never>>() => {};
       ],
     },
     {
-      code: `function quux5(fn: (...args: any) => void): void {}`,
+      code: 'function quux5(fn: (...args: any) => void): void {}',
       options: [{ ignoreRestArgs: true }],
       errors: [
         {
@@ -1009,7 +1127,7 @@ const test = <T extends Partial<never>>() => {};
       ],
     },
     {
-      code: `function quuz5(): ((...args: any) => void) {}`,
+      code: 'function quuz5(): ((...args: any) => void) {}',
       options: [{ ignoreRestArgs: true }],
       errors: [
         {
@@ -1019,6 +1137,61 @@ const test = <T extends Partial<never>>() => {};
         },
       ],
     },
+    {
+      code: 'type Fred5 = (...args: any) => void;',
+      options: [{ ignoreRestArgs: true }],
+      errors: [
+        {
+          messageId: 'unexpectedAny',
+          line: 1,
+          column: 24,
+        },
+      ],
+    },
+    {
+      code: 'type Corge5 = new (...args: any) => void;',
+      options: [{ ignoreRestArgs: true }],
+      errors: [
+        {
+          messageId: 'unexpectedAny',
+          line: 1,
+          column: 29,
+        },
+      ],
+    },
+    {
+      code: 'interface Grault5 { new (...args: any): void; }',
+      options: [{ ignoreRestArgs: true }],
+      errors: [
+        {
+          messageId: 'unexpectedAny',
+          line: 1,
+          column: 35,
+        },
+      ],
+    },
+    {
+      code: 'interface Garply5 { f(...args: any): void; }',
+      options: [{ ignoreRestArgs: true }],
+      errors: [
+        {
+          messageId: 'unexpectedAny',
+          line: 1,
+          column: 32,
+        },
+      ],
+    },
+    {
+      code: 'declare function waldo5(...args: any): void;',
+      options: [{ ignoreRestArgs: true }],
+      errors: [
+        {
+          messageId: 'unexpectedAny',
+          line: 1,
+          column: 34,
+        },
+      ],
+    },
   ] as InvalidTestCase[]).reduce<InvalidTestCase[]>((acc, testCase) => {
     const suggestions = (code: string): SuggestionOutput[] => [
       {