Resignation from the United States Senate

A member of the United States Senate can resign by writing a letter of resignation to the governor of the state that the senator represents. Under Article I, Section 3 of the Constitution of the United States, and under the Seventeenth Amendment, in case of a vacancy in the Senate resulting from resignation, the executive authority of the state (today known in every state as the governor) can make a temporary appointment to fill the vacancy if so authorized by the state legislature.

Source: Wikipedia — Resignation from the United States Senate (CC BY-SA 4.0)