diff --git a/CHANGELOG.md b/CHANGELOG.md
index 89e7f66e80..1c8a1bb9d5 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,9 @@ This change log adheres to standards from [Keep a CHANGELOG](https://keepachange
 ### Changed
 - [Tests] `named`: Run all TypeScript test ([#2427], thanks [@ProdigySim])
 
+### Fixed
+- [`no-unresolved`, `extensions`]: ignore type only exports ([#2436], thanks [@Lukas-Kullmann])
+
 ## [2.26.0] - 2022-04-05
 
 ### Added
diff --git a/src/rules/extensions.js b/src/rules/extensions.js
index 8596cbfd0f..0de8d5a5e6 100644
--- a/src/rules/extensions.js
+++ b/src/rules/extensions.js
@@ -138,7 +138,7 @@ module.exports = {
     function checkFileExtension(source, node) {
       // bail if the declaration doesn't have a source, e.g. "export { foo };", or if it's only partially typed like in an editor
       if (!source || !source.value) return;
-      
+
       const importPathWithQueryString = source.value;
 
       // don't enforce anything on builtins
@@ -164,8 +164,8 @@ module.exports = {
       ) || isScoped(importPath);
 
       if (!extension || !importPath.endsWith(`.${extension}`)) {
-        // ignore type-only imports
-        if (node.importKind === 'type') return;
+        // ignore type-only imports and exports
+        if (node.importKind === 'type' || node.importKind === 'type') return;
         const extensionRequired = isUseOfExtensionRequired(extension, isPackage);
         const extensionForbidden = isUseOfExtensionForbidden(extension);
         if (extensionRequired && !extensionForbidden) {
diff --git a/src/rules/no-unresolved.js b/src/rules/no-unresolved.js
index b9dae97c8e..dafc7cb13f 100644
--- a/src/rules/no-unresolved.js
+++ b/src/rules/no-unresolved.js
@@ -27,8 +27,8 @@ module.exports = {
     const options = context.options[0] || {};
 
     function checkSourceValue(source, node) {
-      // ignore type-only imports
-      if (node.importKind === 'type') {
+      // ignore type-only imports and exports
+      if (node.importKind === 'type' || node.exportKind === 'type') {
         return;
       }
 
diff --git a/tests/src/rules/extensions.js b/tests/src/rules/extensions.js
index cf93fac9f4..82ea7b3b1e 100644
--- a/tests/src/rules/extensions.js
+++ b/tests/src/rules/extensions.js
@@ -613,6 +613,14 @@ describe('TypeScript', () => {
             ],
             parser,
           }),
+          test({
+            code: 'export type T from "./typescript-declare";',
+            options: [
+              'always',
+              { ts: 'never', tsx: 'never', js: 'never', jsx: 'never' },
+            ],
+            parser,
+          }),
         ],
         invalid: [
           test({
@@ -624,6 +632,15 @@ describe('TypeScript', () => {
             ],
             parser,
           }),
+          test({
+            code: 'export T from "./typescript-declare";',
+            errors: ['Missing file extension for "./typescript-declare"'],
+            options: [
+              'always',
+              { ts: 'never', tsx: 'never', js: 'never', jsx: 'never' },
+            ],
+            parser,
+          }),
         ],
       });
     });
diff --git a/tests/src/rules/no-unresolved.js b/tests/src/rules/no-unresolved.js
index c0252ad19d..2efaff38da 100644
--- a/tests/src/rules/no-unresolved.js
+++ b/tests/src/rules/no-unresolved.js
@@ -451,6 +451,10 @@ context('TypeScript', () => {
           code: 'import type { JSONSchema7Type } from "@types/json-schema";',
           parser,
         }),
+        test({
+          code: 'export type { JSONSchema7Type } from "@types/json-schema";',
+          parser,
+        }),
       ],
       invalid: [
         test({
@@ -458,6 +462,11 @@ context('TypeScript', () => {
           errors: [ "Unable to resolve path to module '@types/json-schema'." ],
           parser,
         }),
+        test({
+          code: 'export { JSONSchema7Type } from "@types/json-schema";',
+          errors: [ "Unable to resolve path to module '@types/json-schema'." ],
+          parser,
+        }),
       ],
     });
   });