U.S. Sen. Al Franken will resign from office Jan. 2, and his successor, Lt. Gov. Tina Smith, will be sworn in the following day, a Franken spokesman said Wednesday.

Franken, a Democrat, announced on Dec. 7 that he would resign “in the coming weeks” following allegations by multiple women of sexually inappropriate behavior by Franken.

Minnesota Gov. Mark Dayton, also a Democrat, has named Lt. Gov. Tina Smith as Franken’s successor, as he is empowered to do under the U.S. Constitution and state law. Smith has said she’ll run in a special election in November to serve out the remainder of Franken’s term. State Sen. Karin Housley, a Republican from St. Mary’s Point, has announced she’ll run in the election, which is likely to draw national attention.

The announcement comes after Franken delivered the first of three expected farewell speeches on the floor of the Senate Wednesday.