diff --git a/packages/eslint-plugin/docs/rules/restrict-plus-operands.md b/packages/eslint-plugin/docs/rules/restrict-plus-operands.md
index 7ad23b60763..35d7a984f90 100644
--- a/packages/eslint-plugin/docs/rules/restrict-plus-operands.md
+++ b/packages/eslint-plugin/docs/rules/restrict-plus-operands.md
@@ -22,14 +22,25 @@ var foo = 1n + 1n;
 
 ## Options
 
-This rule has an object option:
+The rule accepts an options object with the following properties:
 
-- `"checkCompoundAssignments": false`: (default) does not check compound assignments (`+=`)
-- `"checkCompoundAssignments": true`
+```ts
+type Options = {
+  // if true, check compound assignments (`+=`)
+  checkCompoundAssignments?: boolean;
+  // if true, 'any' itself and `string`,`bigint`, `number` is allowed.
+  allowAny?: boolean;
+};
+
+const defaults = {
+  checkCompoundAssignments: false,
+  allowAny: false,
+};
+```
 
 ### `checkCompoundAssignments`
 
-Examples of code for the `{ "checkCompoundAssignments": true }` option:
+Examples of code for this rule with `{ checkCompoundAssignments: true }`:
 
 <!--tabs-->
 
@@ -57,6 +68,29 @@ let bar = '';
 bar += 'test';
 ```
 
+### `allowAny`
+
+Examples of code for this rule with `{ allowAny: true }`:
+
+<!--tabs-->
+
+#### ❌ Incorrect
+
+```ts
+var fn = (a: any, b: boolean) => a + b;
+var fn = (a: any, b: []) => a + b;
+var fn = (a: any, b: {}) => a + b;
+```
+
+#### ✅ Correct
+
+```ts
+var fn = (a: any, b: any) => a + b;
+var fn = (a: any, b: string) => a + b;
+var fn = (a: any, b: bigint) => a + b;
+var fn = (a: any, b: number) => a + b;
+```
+
 ## How to Use
 
 ```json
diff --git a/packages/eslint-plugin/src/rules/restrict-plus-operands.ts b/packages/eslint-plugin/src/rules/restrict-plus-operands.ts
index 30c155e3dcd..afcbf9abf2f 100644
--- a/packages/eslint-plugin/src/rules/restrict-plus-operands.ts
+++ b/packages/eslint-plugin/src/rules/restrict-plus-operands.ts
@@ -5,6 +5,7 @@ import * as util from '../util';
 type Options = [
   {
     checkCompoundAssignments?: boolean;
+    allowAny?: boolean;
   },
 ];
 type MessageIds = 'notNumbers' | 'notStrings' | 'notBigInts';
@@ -34,6 +35,9 @@ export default util.createRule<Options, MessageIds>({
           checkCompoundAssignments: {
             type: 'boolean',
           },
+          allowAny: {
+            type: 'boolean',
+          },
         },
       },
     ],
@@ -41,13 +45,14 @@ export default util.createRule<Options, MessageIds>({
   defaultOptions: [
     {
       checkCompoundAssignments: false,
+      allowAny: false,
     },
   ],
-  create(context, [{ checkCompoundAssignments }]) {
+  create(context, [{ checkCompoundAssignments, allowAny }]) {
     const service = util.getParserServices(context);
     const typeChecker = service.program.getTypeChecker();
 
-    type BaseLiteral = 'string' | 'number' | 'bigint' | 'invalid';
+    type BaseLiteral = 'string' | 'number' | 'bigint' | 'invalid' | 'any';
 
     /**
      * Helper function to get base type of node
@@ -82,7 +87,8 @@ export default util.createRule<Options, MessageIds>({
       if (
         stringType === 'number' ||
         stringType === 'string' ||
-        stringType === 'bigint'
+        stringType === 'bigint' ||
+        stringType === 'any'
       ) {
         return stringType;
       }
@@ -108,28 +114,53 @@ export default util.createRule<Options, MessageIds>({
       const leftType = getNodeType(node.left);
       const rightType = getNodeType(node.right);
 
-      if (
-        leftType === 'invalid' ||
-        rightType === 'invalid' ||
-        leftType !== rightType
-      ) {
-        if (leftType === 'string' || rightType === 'string') {
+      if (leftType === rightType) {
+        if (leftType === 'invalid') {
           context.report({
             node,
-            messageId: 'notStrings',
+            messageId: 'notNumbers',
           });
-        } else if (leftType === 'bigint' || rightType === 'bigint') {
+        }
+
+        if (!allowAny && leftType === 'any') {
           context.report({
             node,
-            messageId: 'notBigInts',
+            messageId: 'notNumbers',
           });
-        } else {
+        }
+
+        return;
+      }
+
+      if (leftType === 'any' || rightType === 'any') {
+        if (!allowAny || leftType === 'invalid' || rightType === 'invalid') {
           context.report({
             node,
             messageId: 'notNumbers',
           });
         }
+
+        return;
       }
+
+      if (leftType === 'string' || rightType === 'string') {
+        return context.report({
+          node,
+          messageId: 'notStrings',
+        });
+      }
+
+      if (leftType === 'bigint' || rightType === 'bigint') {
+        return context.report({
+          node,
+          messageId: 'notBigInts',
+        });
+      }
+
+      context.report({
+        node,
+        messageId: 'notNumbers',
+      });
     }
 
     return {
diff --git a/packages/eslint-plugin/tests/rules/restrict-plus-operands.test.ts b/packages/eslint-plugin/tests/rules/restrict-plus-operands.test.ts
index af33e3ad3db..12b7e44657e 100644
--- a/packages/eslint-plugin/tests/rules/restrict-plus-operands.test.ts
+++ b/packages/eslint-plugin/tests/rules/restrict-plus-operands.test.ts
@@ -139,6 +139,46 @@ foo += 'string';
         },
       ],
     },
+    {
+      code: `
+export const f = (a: any, b: any) => a + b;
+      `,
+      options: [
+        {
+          allowAny: true,
+        },
+      ],
+    },
+    {
+      code: `
+export const f = (a: any, b: string) => a + b;
+      `,
+      options: [
+        {
+          allowAny: true,
+        },
+      ],
+    },
+    {
+      code: `
+export const f = (a: any, b: bigint) => a + b;
+      `,
+      options: [
+        {
+          allowAny: true,
+        },
+      ],
+    },
+    {
+      code: `
+export const f = (a: any, b: number) => a + b;
+      `,
+      options: [
+        {
+          allowAny: true,
+        },
+      ],
+    },
   ],
   invalid: [
     {
@@ -515,7 +555,7 @@ function foo<T extends 1>(a: T) {
       `,
       errors: [
         {
-          messageId: 'notStrings',
+          messageId: 'notNumbers',
           line: 4,
           column: 19,
         },
@@ -571,5 +611,125 @@ foo += 0;
         },
       ],
     },
+    {
+      code: `
+const f = (a: any, b: boolean) => a + b;
+      `,
+      options: [
+        {
+          allowAny: true,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'notNumbers',
+          line: 2,
+          column: 35,
+        },
+      ],
+    },
+    {
+      code: `
+const f = (a: any, b: []) => a + b;
+      `,
+      options: [
+        {
+          allowAny: true,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'notNumbers',
+          line: 2,
+          column: 30,
+        },
+      ],
+    },
+
+    {
+      code: `
+const f = (a: any, b: any) => a + b;
+      `,
+      options: [
+        {
+          allowAny: false,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'notNumbers',
+          line: 2,
+          column: 31,
+        },
+      ],
+    },
+    {
+      code: `
+const f = (a: any, b: string) => a + b;
+      `,
+      options: [
+        {
+          allowAny: false,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'notNumbers',
+          line: 2,
+          column: 34,
+        },
+      ],
+    },
+    {
+      code: `
+const f = (a: any, b: bigint) => a + b;
+      `,
+      options: [
+        {
+          allowAny: false,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'notNumbers',
+          line: 2,
+          column: 34,
+        },
+      ],
+    },
+    {
+      code: `
+const f = (a: any, b: number) => a + b;
+      `,
+      options: [
+        {
+          allowAny: false,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'notNumbers',
+          line: 2,
+          column: 34,
+        },
+      ],
+    },
+    {
+      code: `
+const f = (a: any, b: boolean) => a + b;
+      `,
+      options: [
+        {
+          allowAny: false,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'notNumbers',
+          line: 2,
+          column: 35,
+        },
+      ],
+    },
   ],
 });