Harbaugh replaces Brady Hoke, who was fired on Dec. 3 after four seasons at the school and a 5-7 record in 2014.
Harbaugh, 51, and the San Francisco 49ers mutually agreed to part ways on Sunday. Harbaugh spent four seasons with San Francisco, leading the team to three straight NFC Championship game appearances before stumbling to 8-8 this season.
On Saturday, there were multiple reports that Harbaugh had accepted an offer from Michigan to become the school's next football coach. Michigan officials were reportedly in San Francisco this weekend to meet with the head coach.
On Sunday morning, Bruce Feldman of Fox Sports reported that Harbaugh is expected to be introduced at Michigan's men's basketball game on Tuesday. Jay Glazer of Fox Sports also reported Sunday that the Oakland Raiders remain "hopeful" about the chance of hiring Harbaugh. The team is looking to fill its coaching vacancy after firing Dennis Allen in September.
Several names were linked as potential candidates for the Michigan job, including LSU head coach Les Miles, Oklahoma State head Mike Gundy and former Rutgers and Tampa Bay Buccaneers head coach Greg Schiano.
Michigan reportedly reached out to Harbaugh about the position earlier this month but left the conversation convinced that he wanted to stay in the NFL.
After firing Hoke, Michigan interim athletic director Jim Hackett said he wanted to get rid of the word 'Michigan Man' when asked about the search for a new coach. Since former coach Bo Schembechler popularized the term in 1989, only Rich Rodriguez has been hired as Wolverines head coach without previously serving as an assistant at Michigan. Harbaugh played quarterback for four years at Michigan from 1983-1986.
In four years at Michigan, Hoke had a 31-20 record, but the Wolverines' win total declined each season. At Michigan's end-of-the-year football banquet, held a week after his firing, Hoke received a standing ovation from the audience of players and coaches.
- Molly Geary and Scooby Axson