diff --git a/packages/eslint-plugin/docs/rules/explicit-function-return-type.md b/packages/eslint-plugin/docs/rules/explicit-function-return-type.md
index 3a67a7e23721..a5df82f958ab 100644
--- a/packages/eslint-plugin/docs/rules/explicit-function-return-type.md
+++ b/packages/eslint-plugin/docs/rules/explicit-function-return-type.md
@@ -257,6 +257,26 @@ You may pass function/method names you would like this rule to ignore, like so:
 }
 ```
 
+### `allowIIFE`
+
+Examples of code for this rule with `{ allowIIFE: true }`:
+
+#### ❌ Incorrect
+
+```ts
+var func = () => 'foo';
+```
+
+#### ✅ Correct
+
+```ts
+var foo = (() => 'foo')();
+
+var bar = (function () {
+  return 'bar';
+})();
+```
+
 ## When Not To Use It
 
 If you don't wish to prevent calling code from using function return values in unexpected ways, then
diff --git a/packages/eslint-plugin/src/rules/explicit-function-return-type.ts b/packages/eslint-plugin/src/rules/explicit-function-return-type.ts
index 9c91aa6d83d9..254c48a0965c 100644
--- a/packages/eslint-plugin/src/rules/explicit-function-return-type.ts
+++ b/packages/eslint-plugin/src/rules/explicit-function-return-type.ts
@@ -17,6 +17,7 @@ type Options = [
     allowConciseArrowFunctionExpressionsStartingWithVoid?: boolean;
     allowFunctionsWithoutTypeParameters?: boolean;
     allowedNames?: string[];
+    allowIIFEs?: boolean;
   },
 ];
 type MessageIds = 'missingReturnType';
@@ -75,6 +76,11 @@ export default util.createRule<Options, MessageIds>({
             },
             type: 'array',
           },
+          allowIIFEs: {
+            description:
+              'Whether to ignore immediately invoked function expressions (IIFEs).',
+            type: 'boolean',
+          },
         },
         additionalProperties: false,
       },
@@ -88,6 +94,7 @@ export default util.createRule<Options, MessageIds>({
       allowDirectConstAssertionInArrowFunctions: true,
       allowConciseArrowFunctionExpressionsStartingWithVoid: false,
       allowedNames: [],
+      allowIIFEs: false,
     },
   ],
   create(context, [options]) {
@@ -102,6 +109,10 @@ export default util.createRule<Options, MessageIds>({
         return true;
       }
 
+      if (options.allowIIFEs && isIIFE(node)) {
+        return true;
+      }
+
       if (!options.allowedNames?.length) {
         return false;
       }
@@ -149,6 +160,16 @@ export default util.createRule<Options, MessageIds>({
       }
       return false;
     }
+
+    function isIIFE(
+      node:
+        | TSESTree.ArrowFunctionExpression
+        | TSESTree.FunctionExpression
+        | TSESTree.FunctionDeclaration,
+    ): boolean {
+      return node.parent!.type === AST_NODE_TYPES.CallExpression;
+    }
+
     return {
       'ArrowFunctionExpression, FunctionExpression'(
         node: TSESTree.ArrowFunctionExpression | TSESTree.FunctionExpression,
diff --git a/packages/eslint-plugin/tests/rules/explicit-function-return-type.test.ts b/packages/eslint-plugin/tests/rules/explicit-function-return-type.test.ts
index 912242247af7..d3c1a5401926 100644
--- a/packages/eslint-plugin/tests/rules/explicit-function-return-type.test.ts
+++ b/packages/eslint-plugin/tests/rules/explicit-function-return-type.test.ts
@@ -595,6 +595,132 @@ const x: Bar<Foo> = arg1 => arg2 => arg1 + arg2;
         },
       ],
     },
+    {
+      filename: 'test.ts',
+      code: `
+let foo = function (): number {
+  return 1;
+};
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+const foo = (function () {
+  return 1;
+})();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+const foo = (() => {
+  return 1;
+})();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+const foo = ((arg: number): number => {
+  return arg;
+})(0);
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+const foo = (() => (() => 'foo')())();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+let foo = (() => (): string => {
+  return 'foo';
+})()();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+let foo = (() => (): string => {
+  return 'foo';
+})();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+          allowHigherOrderFunctions: false,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+let foo = (() => (): string => {
+  return 'foo';
+})()();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+          allowHigherOrderFunctions: true,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+let foo = (() => (): void => {})()();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+let foo = (() => (() => {})())();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+    },
   ],
   invalid: [
     {
@@ -1477,5 +1603,93 @@ class Foo {
         },
       ],
     },
+    {
+      filename: 'test.ts',
+      code: `
+const foo = (function () {
+  return 'foo';
+})();
+      `,
+      options: [
+        {
+          allowIIFEs: false,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'missingReturnType',
+          line: 2,
+          endLine: 2,
+          column: 14,
+          endColumn: 25,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+const foo = (function () {
+  return () => {
+    return 1;
+  };
+})();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'missingReturnType',
+          line: 3,
+          endLine: 3,
+          column: 10,
+          endColumn: 15,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+let foo = function () {
+  return 'foo';
+};
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'missingReturnType',
+          line: 2,
+          endLine: 2,
+          column: 11,
+          endColumn: 22,
+        },
+      ],
+    },
+    {
+      filename: 'test.ts',
+      code: `
+let foo = (() => () => {})()();
+      `,
+      options: [
+        {
+          allowIIFEs: true,
+        },
+      ],
+      errors: [
+        {
+          messageId: 'missingReturnType',
+          line: 2,
+          endLine: 2,
+          column: 18,
+          endColumn: 23,
+        },
+      ],
+    },
   ],
 });

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