diff --git a/packages/eslint-plugin/docs/rules/no-unsafe-assignment.md b/packages/eslint-plugin/docs/rules/no-unsafe-assignment.md
index 1a452e431eb..64207e5365e 100644
--- a/packages/eslint-plugin/docs/rules/no-unsafe-assignment.md
+++ b/packages/eslint-plugin/docs/rules/no-unsafe-assignment.md
@@ -56,6 +56,16 @@ const x: Set<string[]> = new Set<string[]>();
 const x: Set<Set<Set<string>>> = new Set<Set<Set<string>>>();
 ```
 
+There are cases where the rule allows assignment of `any` to `unknown`.
+
+Example of `any` to `unknown` assignment that are allowed.
+
+```ts
+const x: unknown = y as any;
+const x: unknown[] = y as any[];
+const x: Set<unknown> = y as Set<any>;
+```
+
 ## Related to
 
 - [`no-explicit-any`](./no-explicit-any.md)
diff --git a/packages/eslint-plugin/docs/rules/no-unsafe-return.md b/packages/eslint-plugin/docs/rules/no-unsafe-return.md
index 507abc3dfa2..9810be3cf16 100644
--- a/packages/eslint-plugin/docs/rules/no-unsafe-return.md
+++ b/packages/eslint-plugin/docs/rules/no-unsafe-return.md
@@ -69,6 +69,20 @@ type TAssign = () => Set<string>;
 const assignability2: TAssign = () => new Set(['foo']);
 ```
 
+There are cases where the rule allows to return `any` to `unknown`.
+
+Examples of `any` to `unknown` return that are allowed.
+
+```ts
+function foo1(): unknown {
+  return JSON.parse(singleObjString); // Return type for JSON.parse is any.
+}
+
+function foo2(): unknown[] {
+  return [] as any[];
+}
+```
+
 ## Related to
 
 - [`no-explicit-any`](./no-explicit-any.md)
diff --git a/packages/eslint-plugin/src/rules/no-unsafe-assignment.ts b/packages/eslint-plugin/src/rules/no-unsafe-assignment.ts
index 21e646483bc..4a8f2a9ea23 100644
--- a/packages/eslint-plugin/src/rules/no-unsafe-assignment.ts
+++ b/packages/eslint-plugin/src/rules/no-unsafe-assignment.ts
@@ -238,6 +238,11 @@ export default util.createRule({
       );
 
       if (util.isTypeAnyType(senderType)) {
+        // handle cases when we assign any ==> unknown.
+        if (util.isTypeUnknownType(receiverType)) {
+          return false;
+        }
+
         context.report({
           node: reportingNode,
           messageId: 'anyAssignment',
diff --git a/packages/eslint-plugin/src/rules/no-unsafe-return.ts b/packages/eslint-plugin/src/rules/no-unsafe-return.ts
index b0168dc6f50..c2366bc96f2 100644
--- a/packages/eslint-plugin/src/rules/no-unsafe-return.ts
+++ b/packages/eslint-plugin/src/rules/no-unsafe-return.ts
@@ -58,16 +58,6 @@ export default util.createRule({
     ): void {
       const tsNode = esTreeNodeToTSNodeMap.get(returnNode);
       const anyType = util.isAnyOrAnyArrayTypeDiscriminated(tsNode, checker);
-      if (anyType !== util.AnyType.Safe) {
-        return context.report({
-          node: reportingNode,
-          messageId: 'unsafeReturn',
-          data: {
-            type: anyType === util.AnyType.Any ? 'any' : 'any[]',
-          },
-        });
-      }
-
       const functionNode = getParentFunctionNode(returnNode);
       /* istanbul ignore if */ if (!functionNode) {
         return;
@@ -91,6 +81,35 @@ export default util.createRule({
         functionType = checker.getTypeAtLocation(functionTSNode);
       }
 
+      if (anyType !== util.AnyType.Safe) {
+        // Allow cases when the declared return type of the function is either unknown or unknown[]
+        // and the function is returning any or any[].
+        for (const signature of functionType.getCallSignatures()) {
+          const functionReturnType = signature.getReturnType();
+          if (
+            anyType === util.AnyType.Any &&
+            util.isTypeUnknownType(functionReturnType)
+          ) {
+            return;
+          }
+          if (
+            anyType === util.AnyType.AnyArray &&
+            util.isTypeUnknownArrayType(functionReturnType, checker)
+          ) {
+            return;
+          }
+        }
+
+        // If the function return type was not unknown/unknown[], mark usage as unsafeReturn.
+        return context.report({
+          node: reportingNode,
+          messageId: 'unsafeReturn',
+          data: {
+            type: anyType === util.AnyType.Any ? 'any' : 'any[]',
+          },
+        });
+      }
+
       for (const signature of functionType.getCallSignatures()) {
         const functionReturnType = signature.getReturnType();
         if (returnNodeType === functionReturnType) {
diff --git a/packages/eslint-plugin/src/util/types.ts b/packages/eslint-plugin/src/util/types.ts
index d030b829cd4..d29349f812f 100644
--- a/packages/eslint-plugin/src/util/types.ts
+++ b/packages/eslint-plugin/src/util/types.ts
@@ -365,6 +365,22 @@ export function isTypeAnyArrayType(
   );
 }
 
+/**
+ * @returns true if the type is `unknown[]`
+ */
+export function isTypeUnknownArrayType(
+  type: ts.Type,
+  checker: ts.TypeChecker,
+): boolean {
+  return (
+    checker.isArrayType(type) &&
+    isTypeUnknownType(
+      // getTypeArguments was only added in TS3.7
+      getTypeArguments(type, checker)[0],
+    )
+  );
+}
+
 export const enum AnyType {
   Any,
   AnyArray,
@@ -403,8 +419,15 @@ export function isUnsafeAssignment(
   receiver: ts.Type,
   checker: ts.TypeChecker,
 ): false | { sender: ts.Type; receiver: ts.Type } {
-  if (isTypeAnyType(type) && !isTypeAnyType(receiver)) {
-    return { sender: type, receiver };
+  if (isTypeAnyType(type)) {
+    // Allow assignment of any ==> unknown.
+    if (isTypeUnknownType(receiver)) {
+      return false;
+    }
+
+    if (!isTypeAnyType(receiver)) {
+      return { sender: type, receiver };
+    }
   }
 
   if (isTypeReference(type) && isTypeReference(receiver)) {
diff --git a/packages/eslint-plugin/tests/rules/no-unsafe-assignment.test.ts b/packages/eslint-plugin/tests/rules/no-unsafe-assignment.test.ts
index 708969310ed..edfa8abadd2 100644
--- a/packages/eslint-plugin/tests/rules/no-unsafe-assignment.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-unsafe-assignment.test.ts
@@ -119,6 +119,15 @@ declare function Foo(props: Props): never;
       `,
       filename: 'react.tsx',
     },
+    `
+      const x: unknown = y as any;
+    `,
+    `
+      const x: unknown[] = y as any[];
+    `,
+    `
+      const x: Set<unknown> = y as Set<any>;
+    `,
   ],
   invalid: [
     ...batchedSingleLineTests({
diff --git a/packages/eslint-plugin/tests/rules/no-unsafe-return.test.ts b/packages/eslint-plugin/tests/rules/no-unsafe-return.test.ts
index 91627f91b02..7d7777e4663 100644
--- a/packages/eslint-plugin/tests/rules/no-unsafe-return.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-unsafe-return.test.ts
@@ -77,6 +77,21 @@ function foo(): Set<number> {
         return x;
       }
     `,
+    `
+      function fn<T extends any>(x: T): unknown {
+        return x as any;
+      }
+    `,
+    `
+      function fn<T extends any>(x: T): unknown[] {
+        return x as any[];
+      }
+    `,
+    `
+      function fn<T extends any>(x: T): Set<unknown> {
+        return x as Set<any>;
+      }
+    `,
   ],
   invalid: [
     ...batchedSingleLineTests({
diff --git a/packages/eslint-plugin/tests/util/isUnsafeAssignment.test.ts b/packages/eslint-plugin/tests/util/isUnsafeAssignment.test.ts
index 3862b38902c..efe1fe9d1ba 100644
--- a/packages/eslint-plugin/tests/util/isUnsafeAssignment.test.ts
+++ b/packages/eslint-plugin/tests/util/isUnsafeAssignment.test.ts
@@ -166,5 +166,29 @@ describe('isUnsafeAssignment', () => {
 
       expect(isUnsafeAssignment(sender, receiver, checker)).toBeFalsy();
     });
+
+    it('any to a unknown', () => {
+      const { sender, receiver, checker } = getTypes(
+        'const test: unknown = [] as any;',
+      );
+
+      expect(isUnsafeAssignment(sender, receiver, checker)).toBeFalsy();
+    });
+
+    it('any[] in a generic position to a unknown[]', () => {
+      const { sender, receiver, checker } = getTypes(
+        'const test: unknown[] = [] as any[]',
+      );
+
+      expect(isUnsafeAssignment(sender, receiver, checker)).toBeFalsy();
+    });
+
+    it('any in a generic position to a unknown (nested)', () => {
+      const { sender, receiver, checker } = getTypes(
+        'const test: Set<Set<Set<unknown>>> = new Set<Set<Set<any>>>();',
+      );
+
+      expect(isUnsafeAssignment(sender, receiver, checker)).toBeFalsy();
+    });
   });
 });