diff --git a/packages/eslint-plugin/docs/rules/promise-function-async.md b/packages/eslint-plugin/docs/rules/promise-function-async.md
index c64c25c11b5a..a0b702d6bd68 100644
--- a/packages/eslint-plugin/docs/rules/promise-function-async.md
+++ b/packages/eslint-plugin/docs/rules/promise-function-async.md
@@ -36,6 +36,7 @@ async function functionDeturnsPromise() {
 
 Options may be provided as an object with:
 
+- `allowAny` to indicate that `any` or `unknown` shouldn't be considered Promises (`true` by default).
 - `allowedPromiseNames` to indicate any extra names of classes or interfaces to be considered Promises when returned.
 
 In addition, each of the following properties may be provided, and default to `true`:
@@ -50,6 +51,7 @@ In addition, each of the following properties may be provided, and default to `t
   "@typescript-eslint/promise-function-async": [
     "error",
     {
+      "allowAny": true,
       "allowedPromiseNames": ["Thenable"],
       "checkArrowFunctions": true,
       "checkFunctionDeclarations": true,
diff --git a/packages/eslint-plugin/src/rules/promise-function-async.ts b/packages/eslint-plugin/src/rules/promise-function-async.ts
index 885580c493fa..44214d44dd5c 100644
--- a/packages/eslint-plugin/src/rules/promise-function-async.ts
+++ b/packages/eslint-plugin/src/rules/promise-function-async.ts
@@ -1,8 +1,11 @@
+import ts from 'typescript';
+import { isTypeFlagSet } from 'tsutils';
 import { TSESTree } from '@typescript-eslint/experimental-utils';
 import * as util from '../util';
 
 type Options = [
   {
+    allowAny?: boolean;
     allowedPromiseNames?: string[];
     checkArrowFunctions?: boolean;
     checkFunctionDeclarations?: boolean;
@@ -29,6 +32,9 @@ export default util.createRule<Options, MessageIds>({
       {
         type: 'object',
         properties: {
+          allowAny: {
+            type: 'boolean',
+          },
           allowedPromiseNames: {
             type: 'array',
             items: {
@@ -54,6 +60,7 @@ export default util.createRule<Options, MessageIds>({
   },
   defaultOptions: [
     {
+      allowAny: true,
       allowedPromiseNames: [],
       checkArrowFunctions: true,
       checkFunctionDeclarations: true,
@@ -65,6 +72,7 @@ export default util.createRule<Options, MessageIds>({
     context,
     [
       {
+        allowAny,
         allowedPromiseNames,
         checkArrowFunctions,
         checkFunctionDeclarations,
@@ -90,6 +98,12 @@ export default util.createRule<Options, MessageIds>({
       }
       const returnType = checker.getReturnTypeOfSignature(signatures[0]);
 
+      if (
+        allowAny &&
+        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..d3b84bbdd313 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 0;
+}
+    `,
+    `
+function returnsUnknown(): unknown {
+  return 0;
+}
+    `,
+    `
 const nonAsyncNonPromiseArrowFunction = (n: number) => n;
     `,
     `
@@ -31,6 +41,10 @@ const asyncPromiseFunctionExpressionB = async function() { return new Promise<vo
 class Test {
   public nonAsyncNonPromiseArrowFunction = (n: number) => n;
 
+  public constructor() {
+    return 0 as any;
+  }
+
   public nonAsyncNonPromiseMethod() {
     return 0;
   }
@@ -42,6 +56,14 @@ class Test {
   public async asyncPromiseMethodB() {
     return new Promise<void>();
   }
+
+  public get getterThatReturnsAny() {
+    return 0 as any;
+  }
+
+  public set setterThatReturnsAny(value: number) {
+    return 0 as any;
+  }
 }
     `,
     // https://github.com/typescript-eslint/typescript-eslint/issues/227
@@ -287,5 +309,41 @@ const returnAllowedType = () => new PromiseType();
         },
       ],
     },
+    {
+      code: `
+function returnsAny(): any {
+  return 0;
+}
+`,
+      options: [
+        {
+          allowAny: false,
+        },
+      ],
+      errors: [
+        {
+          line: 2,
+          messageId,
+        },
+      ],
+    },
+    {
+      code: `
+function returnsUnknown(): unknown {
+  return 0;
+}
+`,
+      options: [
+        {
+          allowAny: false,
+        },
+      ],
+      errors: [
+        {
+          line: 2,
+          messageId,
+        },
+      ],
+    },
   ],
 });