Baucus has previously announced that he would not run for reelection in 2014.
The veteran Montana Democrat would succeed Gary Locke, the current U.S. ambassador to China, if confirmed by the Senate.
Montana Gov. Steve Bullock (D) will appoint a replacement to finish out the remaining year of Baucus's time in office.
Bullock is expected to pick Lt. Gov. John Walsh (D), currently running in the Democratic primary for Senate, to finish Baucus' term, according to a national Democratic official.
This post was updated.