diff --git a/doc/api/net.md b/doc/api/net.md
index 231dde85428a9c..50ea9ab6c45bc3 100644
--- a/doc/api/net.md
+++ b/doc/api/net.md
@@ -496,6 +496,10 @@ it to interact with the client.
 ### `new net.Socket([options])`
 <!-- YAML
 added: v0.3.4
+changes:
+  - version: REPLACEME
+    pr-url: https://github.com/nodejs/node/pull/37735
+    description: AbortSignal support was added.
 -->
 
 * `options` {Object} Available options are:
@@ -508,6 +512,8 @@ added: v0.3.4
     otherwise ignored. **Default:** `false`.
   * `writable` {boolean} Allow writes on the socket when an `fd` is passed,
     otherwise ignored. **Default:** `false`.
+  * `signal` {AbortSignal} An Abort signal that may be used to destroy the
+    socket.
 * Returns: {net.Socket}
 
 Creates a new socket object.
diff --git a/lib/_tls_wrap.js b/lib/_tls_wrap.js
index c31d69117c6bd4..869bbda42f7898 100644
--- a/lib/_tls_wrap.js
+++ b/lib/_tls_wrap.js
@@ -515,6 +515,7 @@ function TLSSocket(socket, opts) {
     manualStart: true,
     highWaterMark: tlsOptions.highWaterMark,
     onread: !socket ? tlsOptions.onread : null,
+    signal: tlsOptions.signal,
   }]);
 
   // Proxy for API compatibility
@@ -1627,6 +1628,7 @@ exports.connect = function connect(...args) {
     pskCallback: options.pskCallback,
     highWaterMark: options.highWaterMark,
     onread: options.onread,
+    signal: options.signal,
   });
 
   tlssock[kConnectOptions] = options;
diff --git a/test/parallel/test-http2-client-destroy.js b/test/parallel/test-http2-client-destroy.js
index 52b0744cd2190d..189a6f55a596da 100644
--- a/test/parallel/test-http2-client-destroy.js
+++ b/test/parallel/test-http2-client-destroy.js
@@ -240,3 +240,48 @@ const { getEventListeners } = require('events');
     req.on('close', common.mustCall(() => server.close()));
   }));
 }
+
+
+// Destroy ClientHttpSession with AbortSignal
+{
+  function testH2ConnectAbort(secure) {
+    const server = secure ? h2.createSecureServer() : h2.createServer();
+    const controller = new AbortController();
+
+    server.on('stream', common.mustNotCall());
+    server.listen(0, common.mustCall(() => {
+      const { signal } = controller;
+      const protocol = secure ? 'https' : 'http';
+      const client = h2.connect(`${protocol}://localhost:${server.address().port}`, {
+        signal,
+      });
+      client.on('close', common.mustCall());
+      assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+
+      client.on('error', common.mustCall(common.mustCall((err) => {
+        assert.strictEqual(err.code, 'ABORT_ERR');
+        assert.strictEqual(err.name, 'AbortError');
+      })));
+
+      const req = client.request({}, {});
+      assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+
+      req.on('error', common.mustCall((err) => {
+        assert.strictEqual(err.code, 'ERR_HTTP2_STREAM_CANCEL');
+        assert.strictEqual(err.name, 'Error');
+        assert.strictEqual(req.aborted, false);
+        assert.strictEqual(req.destroyed, true);
+      }));
+      req.on('close', common.mustCall(() => server.close()));
+
+      assert.strictEqual(req.aborted, false);
+      assert.strictEqual(req.destroyed, false);
+      // Signal listener attached
+      assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+
+      controller.abort();
+    }));
+  }
+  testH2ConnectAbort(false);
+  testH2ConnectAbort(true);
+}
diff --git a/test/parallel/test-https-abortcontroller.js b/test/parallel/test-https-abortcontroller.js
index 19aa9a6fca2bdf..420bf9217e8f5b 100644
--- a/test/parallel/test-https-abortcontroller.js
+++ b/test/parallel/test-https-abortcontroller.js
@@ -14,6 +14,7 @@ const options = {
   cert: fixtures.readKey('agent1-cert.pem')
 };
 
+// Check async post-aborted
 (async () => {
   const { port, server } = await new Promise((resolve) => {
     const server = https.createServer(options, () => {});
@@ -38,3 +39,57 @@ const options = {
     server.close();
   }
 })().then(common.mustCall());
+
+// Check sync post-aborted signal
+(async () => {
+  const { port, server } = await new Promise((resolve) => {
+    const server = https.createServer(options, () => {});
+    server.listen(0, () => resolve({ port: server.address().port, server }));
+  });
+  try {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const req = https.request({
+      host: 'localhost',
+      port,
+      path: '/',
+      method: 'GET',
+      rejectUnauthorized: false,
+      signal,
+    });
+    assert.strictEqual(getEventListeners(ac.signal, 'abort').length, 1);
+    ac.abort();
+    const [ err ] = await once(req, 'error');
+    assert.strictEqual(err.name, 'AbortError');
+    assert.strictEqual(err.code, 'ABORT_ERR');
+  } finally {
+    server.close();
+  }
+})().then(common.mustCall());
+
+// Check pre-aborted signal
+(async () => {
+  const { port, server } = await new Promise((resolve) => {
+    const server = https.createServer(options, () => {});
+    server.listen(0, () => resolve({ port: server.address().port, server }));
+  });
+  try {
+    const ac = new AbortController();
+    const { signal } = ac;
+    ac.abort();
+    const req = https.request({
+      host: 'localhost',
+      port,
+      path: '/',
+      method: 'GET',
+      rejectUnauthorized: false,
+      signal,
+    });
+    assert.strictEqual(getEventListeners(ac.signal, 'abort').length, 0);
+    const [ err ] = await once(req, 'error');
+    assert.strictEqual(err.name, 'AbortError');
+    assert.strictEqual(err.code, 'ABORT_ERR');
+  } finally {
+    server.close();
+  }
+})().then(common.mustCall());
diff --git a/test/parallel/test-https-agent-abort-controller.js b/test/parallel/test-https-agent-abort-controller.js
new file mode 100644
index 00000000000000..14331e7036d66d
--- /dev/null
+++ b/test/parallel/test-https-agent-abort-controller.js
@@ -0,0 +1,87 @@
+'use strict';
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+
+const assert = require('assert');
+const https = require('https');
+const { once } = require('events');
+const Agent = https.Agent;
+const fixtures = require('../common/fixtures');
+
+const { getEventListeners } = require('events');
+const agent = new Agent();
+
+const options = {
+  key: fixtures.readKey('agent1-key.pem'),
+  cert: fixtures.readKey('agent1-cert.pem')
+};
+
+const server = https.createServer(options);
+
+server.listen(0, common.mustCall(async () => {
+  const port = server.address().port;
+  const host = 'localhost';
+  const options = {
+    port: port,
+    host: host,
+    rejectUnauthorized: false,
+    _agentKey: agent.getName({ port, host })
+  };
+
+  async function postCreateConnection() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const connection = agent.createConnection({ ...options, signal });
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    ac.abort();
+    const [err] = await once(connection, 'error');
+    assert.strictEqual(err.name, 'AbortError');
+  }
+
+  async function preCreateConnection() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    ac.abort();
+    const connection = agent.createConnection({ ...options, signal });
+    const [err] = await once(connection, 'error');
+    assert.strictEqual(err.name, 'AbortError');
+  }
+
+
+  async function agentAsParam() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const request = https.get({
+      port: server.address().port,
+      path: '/hello',
+      agent: agent,
+      signal,
+    });
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    ac.abort();
+    const [err] = await once(request, 'error');
+    assert.strictEqual(err.name, 'AbortError');
+  }
+
+  async function agentAsParamPreAbort() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    ac.abort();
+    const request = https.get({
+      port: server.address().port,
+      path: '/hello',
+      agent: agent,
+      signal,
+    });
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 0);
+    const [err] = await once(request, 'error');
+    assert.strictEqual(err.name, 'AbortError');
+  }
+
+  await postCreateConnection();
+  await preCreateConnection();
+  await agentAsParam();
+  await agentAsParamPreAbort();
+  server.close();
+}));
diff --git a/test/parallel/test-net-connect-abort-controller.js b/test/parallel/test-net-connect-abort-controller.js
new file mode 100644
index 00000000000000..9c259cc3fc2c15
--- /dev/null
+++ b/test/parallel/test-net-connect-abort-controller.js
@@ -0,0 +1,96 @@
+'use strict';
+const common = require('../common');
+const net = require('net');
+const assert = require('assert');
+const server = net.createServer();
+const { getEventListeners, once } = require('events');
+
+const liveConnections = new Set();
+
+server.listen(0, common.mustCall(async () => {
+  const port = server.address().port;
+  const host = 'localhost';
+  const socketOptions = (signal) => ({ port, host, signal });
+  server.on('connection', (connection) => {
+    liveConnections.add(connection);
+    connection.on('close', () => {
+      liveConnections.delete(connection);
+    });
+  });
+
+  const assertAbort = async (socket, testName) => {
+    try {
+      await once(socket, 'close');
+      assert.fail(`close ${testName} should have thrown`);
+    } catch (err) {
+      assert.strictEqual(err.name, 'AbortError');
+    }
+  };
+
+  async function postAbort() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const socket = net.connect(socketOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    ac.abort();
+    await assertAbort(socket, 'postAbort');
+  }
+
+  async function preAbort() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    ac.abort();
+    const socket = net.connect(socketOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 0);
+    await assertAbort(socket, 'preAbort');
+  }
+
+  async function tickAbort() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    setImmediate(() => ac.abort());
+    const socket = net.connect(socketOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    await assertAbort(socket, 'tickAbort');
+  }
+
+  async function testConstructor() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    ac.abort();
+    const socket = new net.Socket(socketOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 0);
+    await assertAbort(socket, 'testConstructor');
+  }
+
+  async function testConstructorPost() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const socket = new net.Socket(socketOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    ac.abort();
+    await assertAbort(socket, 'testConstructorPost');
+  }
+
+  async function testConstructorPostTick() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const socket = new net.Socket(socketOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    setImmediate(() => ac.abort());
+    await assertAbort(socket, 'testConstructorPostTick');
+  }
+
+  await postAbort();
+  await preAbort();
+  await tickAbort();
+  await testConstructor();
+  await testConstructorPost();
+  await testConstructorPostTick();
+
+  // Killing the net.socket without connecting hangs the server.
+  for (const connection of liveConnections) {
+    connection.destroy();
+  }
+  server.close(common.mustCall());
+}));
diff --git a/test/parallel/test-tls-connect-abort-controller.js b/test/parallel/test-tls-connect-abort-controller.js
new file mode 100644
index 00000000000000..f9a37f1603a7e3
--- /dev/null
+++ b/test/parallel/test-tls-connect-abort-controller.js
@@ -0,0 +1,97 @@
+'use strict';
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+
+const tls = require('tls');
+const assert = require('assert');
+const fixtures = require('../common/fixtures');
+const { getEventListeners, once } = require('events');
+
+const serverOptions = {
+  key: fixtures.readKey('agent1-key.pem'),
+  cert: fixtures.readKey('agent1-cert.pem')
+};
+const server = tls.createServer(serverOptions);
+server.listen(0, common.mustCall(async () => {
+  const port = server.address().port;
+  const host = 'localhost';
+  const connectOptions = (signal) => ({
+    port,
+    host,
+    signal,
+    rejectUnauthorized: false,
+  });
+
+  const assertAbort = async (socket, testName) => {
+    try {
+      await once(socket, 'close');
+      assert.fail(`close ${testName} should have thrown`);
+    } catch (err) {
+      assert.strictEqual(err.name, 'AbortError');
+    }
+  };
+
+  async function postAbort() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const socket = tls.connect(connectOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    ac.abort();
+    await assertAbort(socket, 'postAbort');
+  }
+
+  async function preAbort() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    ac.abort();
+    const socket = tls.connect(connectOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 0);
+    await assertAbort(socket, 'preAbort');
+  }
+
+  async function tickAbort() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const socket = tls.connect(connectOptions(signal));
+    setImmediate(() => ac.abort());
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    await assertAbort(socket, 'tickAbort');
+  }
+
+  async function testConstructor() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    ac.abort();
+    const socket = new tls.TLSSocket(undefined, connectOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 0);
+    await assertAbort(socket, 'testConstructor');
+  }
+
+  async function testConstructorPost() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const socket = new tls.TLSSocket(undefined, connectOptions(signal));
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    ac.abort();
+    await assertAbort(socket, 'testConstructorPost');
+  }
+
+  async function testConstructorPostTick() {
+    const ac = new AbortController();
+    const { signal } = ac;
+    const socket = new tls.TLSSocket(undefined, connectOptions(signal));
+    setImmediate(() => ac.abort());
+    assert.strictEqual(getEventListeners(signal, 'abort').length, 1);
+    await assertAbort(socket, 'testConstructorPostTick');
+  }
+
+  await postAbort();
+  await preAbort();
+  await tickAbort();
+  await testConstructor();
+  await testConstructorPost();
+  await testConstructorPostTick();
+
+  server.close(common.mustCall());
+}));