diff --git a/lib/init/config-file.js b/lib/init/config-file.js
index fc62b81525e..4c648ac0551 100644
--- a/lib/init/config-file.js
+++ b/lib/init/config-file.js
@@ -117,6 +117,7 @@ function writeJSConfigFile(config, filePath) {
 function write(config, filePath) {
     switch (path.extname(filePath)) {
         case ".js":
+        case ".cjs":
             writeJSConfigFile(config, filePath);
             break;
 
diff --git a/lib/init/config-initializer.js b/lib/init/config-initializer.js
index 8cc09b6a960..3c7f2ba0944 100644
--- a/lib/init/config-initializer.js
+++ b/lib/init/config-initializer.js
@@ -12,6 +12,7 @@
 
 const util = require("util"),
     path = require("path"),
+    fs = require("fs"),
     enquirer = require("enquirer"),
     ProgressBar = require("progress"),
     semver = require("semver"),
@@ -48,6 +49,16 @@ function writeFile(config, format) {
         extname = ".yml";
     } else if (format === "JSON") {
         extname = ".json";
+    } else if (format === "JavaScript") {
+        const pkgJSONPath = npmUtils.findPackageJson();
+
+        if (pkgJSONPath) {
+            const pkgJSONContents = JSON.parse(fs.readFileSync(pkgJSONPath, "utf8"));
+
+            if (pkgJSONContents.type === "module") {
+                extname = ".cjs";
+            }
+        }
     }
 
     const installedESLint = config.installedESLint;
@@ -684,6 +695,7 @@ const init = {
     hasESLintVersionConflict,
     installModules,
     processAnswers,
+    writeFile,
     /* istanbul ignore next */initializeConfig() {
         return promptUser();
     }
diff --git a/lib/init/npm-utils.js b/lib/init/npm-utils.js
index 555ea2b2b28..35191cc0876 100644
--- a/lib/init/npm-utils.js
+++ b/lib/init/npm-utils.js
@@ -172,6 +172,7 @@ function checkPackageJson(startDir) {
 module.exports = {
     installSyncSaveDev,
     fetchPeerDependencies,
+    findPackageJson,
     checkDeps,
     checkDevDeps,
     checkPackageJson
diff --git a/tests/lib/init/config-initializer.js b/tests/lib/init/config-initializer.js
index 10a67fe0ab9..81e4e52faaa 100644
--- a/tests/lib/init/config-initializer.js
+++ b/tests/lib/init/config-initializer.js
@@ -27,6 +27,8 @@ const proxyquire = require("proxyquire").noPreserveCache();
 //------------------------------------------------------------------------------
 
 let answers = {};
+let pkgJSONContents = {};
+let pkgJSONPath = "";
 
 describe("configInitializer", () => {
 
@@ -455,4 +457,121 @@ describe("configInitializer", () => {
             });
         });
     });
+
+    describe("writeFile()", () => {
+
+        beforeEach(() => {
+            answers = {
+                purpose: "style",
+                source: "prompt",
+                extendDefault: true,
+                indent: 2,
+                quotes: "single",
+                linebreak: "unix",
+                semi: true,
+                moduleType: "esm",
+                es6Globals: true,
+                env: ["browser"],
+                format: "JSON"
+            };
+
+            pkgJSONContents = {
+                name: "config-initializer",
+                version: "1.0.0"
+            };
+
+            process.chdir(fixtureDir);
+
+            pkgJSONPath = path.resolve(fixtureDir, "package.json");
+        });
+
+        afterEach(() => {
+            process.chdir(originalDir);
+        });
+
+        it("should create .eslintrc.json", () => {
+            const config = init.processAnswers(answers);
+            const filePath = path.resolve(fixtureDir, ".eslintrc.json");
+
+            fs.writeFileSync(pkgJSONPath, JSON.stringify(pkgJSONContents));
+
+            init.writeFile(config, answers.format);
+
+            assert.isTrue(fs.existsSync(filePath));
+
+            fs.unlinkSync(filePath);
+            fs.unlinkSync(pkgJSONPath);
+        });
+
+        it("should create .eslintrc.js", () => {
+            answers.format = "JavaScript";
+
+            const config = init.processAnswers(answers);
+            const filePath = path.resolve(fixtureDir, ".eslintrc.js");
+
+            fs.writeFileSync(pkgJSONPath, JSON.stringify(pkgJSONContents));
+
+            init.writeFile(config, answers.format);
+
+            assert.isTrue(fs.existsSync(filePath));
+
+            fs.unlinkSync(filePath);
+            fs.unlinkSync(pkgJSONPath);
+        });
+
+        it("should create .eslintrc.yml", () => {
+            answers.format = "YAML";
+
+            const config = init.processAnswers(answers);
+            const filePath = path.resolve(fixtureDir, ".eslintrc.yml");
+
+            fs.writeFileSync(pkgJSONPath, JSON.stringify(pkgJSONContents));
+
+            init.writeFile(config, answers.format);
+
+            assert.isTrue(fs.existsSync(filePath));
+
+            fs.unlinkSync(filePath);
+            fs.unlinkSync(pkgJSONPath);
+        });
+
+        // For https://github.com/eslint/eslint/issues/14137
+        it("should create .eslintrc.cjs", () => {
+            answers.format = "JavaScript";
+
+            // create package.json with "type": "module"
+            pkgJSONContents.type = "module";
+
+            fs.writeFileSync(pkgJSONPath, JSON.stringify(pkgJSONContents));
+
+            const config = init.processAnswers(answers);
+            const filePath = path.resolve(fixtureDir, ".eslintrc.cjs");
+
+            init.writeFile(config, answers.format);
+
+            assert.isTrue(fs.existsSync(filePath));
+
+            fs.unlinkSync(filePath);
+            fs.unlinkSync(pkgJSONPath);
+        });
+
+        it("should create .eslintrc.json even with type: 'module'", () => {
+            answers.format = "JSON";
+
+            // create package.json with "type": "module"
+            pkgJSONContents.type = "module";
+
+            fs.writeFileSync(pkgJSONPath, JSON.stringify(pkgJSONContents));
+
+            const config = init.processAnswers(answers);
+            const filePath = path.resolve(fixtureDir, ".eslintrc.json");
+
+            init.writeFile(config, answers.format);
+
+            assert.isTrue(fs.existsSync(filePath));
+
+            fs.unlinkSync(filePath);
+            fs.unlinkSync(pkgJSONPath);
+        });
+    });
 });