How did the Supreme Court and Courts of Appeals get in the Judicial branch?

Article III, Section 1, of the Constitution prescribes creation of the US Supreme Court, and gives Congress the authority to establish lower courts, as necessary. Congress formally established the federal judiciary in the Judiciary Act of 1789.

The Framers of the Constitution placed the court system in the Judicial branch because "Judicial" refers to "judging," making the Judicial branch the most appropriate for the courts.

Article III

Section 1. The judicial power of the United States, shall be vested in one Supreme Court, and in such inferior courts as the Congress may from time to time ordain and establish. The judges, both of the supreme and inferior courts, shall hold their offices during good behaviour, and shall, at stated times, receive for their services, a compensation, which shall not be diminished during their continuance in office.