Walsh's announcement, made in a Web video, gave Democrats their first big-name recruit in the race for the open seat after former Gov. Brian Schweitzer said he wouldn't run, The Washington Post reported.
Walsh's video stressed his service in Iraq and his political newcomer status. He was the adjutant general of Montana's National Guard before being selected as current Gov. Steve Bullock's running mate in the 2012 election.
Republican freshman Rep. Steve Daines is still considering whether to run for the Senate seat, the Post said. The GOP field currently is led by former Montana state Sen. Corey Stapleton.
The seat is considered a key pickup opportunity for Republicans after Baucus announced his retirement.