diff --git a/packages/eslint-plugin/src/rules/promise-function-async.ts b/packages/eslint-plugin/src/rules/promise-function-async.ts
index 885580c493fa..78854f58bfaa 100644
--- a/packages/eslint-plugin/src/rules/promise-function-async.ts
+++ b/packages/eslint-plugin/src/rules/promise-function-async.ts
@@ -1,3 +1,5 @@
+import ts from 'typescript';
+import { isTypeFlagSet } from 'tsutils';
 import { TSESTree } from '@typescript-eslint/experimental-utils';
 import * as util from '../util';
 
@@ -90,6 +92,9 @@ export default util.createRule<Options, MessageIds>({
       }
       const returnType = checker.getReturnTypeOfSignature(signatures[0]);
 
+      if (isTypeFlagSet(returnType, ts.TypeFlags.Any | ts.TypeFlags.Unknown)) {
+        return;
+      }
       if (!util.containsTypeByName(returnType, allAllowedPromiseNames)) {
         return;
       }
diff --git a/packages/eslint-plugin/tests/rules/promise-function-async.test.ts b/packages/eslint-plugin/tests/rules/promise-function-async.test.ts
index 3910cea56042..4da2cf4109d8 100644
--- a/packages/eslint-plugin/tests/rules/promise-function-async.test.ts
+++ b/packages/eslint-plugin/tests/rules/promise-function-async.test.ts
@@ -16,6 +16,16 @@ const ruleTester = new RuleTester({
 ruleTester.run('promise-function-async', rule, {
   valid: [
     `
+function returnsAny(): any {
+  return 1;
+}
+    `,
+    `
+function returnsUnknown(): unknown {
+  return 1;
+}
+    `,
+    `
 const nonAsyncNonPromiseArrowFunction = (n: number) => n;
     `,
     `