The Appointments Clause gives the executive branch and the President, not Congress, the power to appoint federal officials. The President has the power to appoint federal judges, ambassadors, and other "principal officers” of the United States, subject to Senate confirmation of such appointments.

Which branch of government nominates ambassadors?

The United States Constitution provides that the president "shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the Supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided ...

Which branch does the appointing?

The President is responsible for implementing and enforcing the laws written by Congress and, to that end, appoints the heads of the federal agencies, including the Cabinet. The Vice President is also part of the Executive Branch, ready to assume the Presidency should the need arise.