Harbaugh, who played for the school at quarterback in the mid-1980s, was allowed to leave the San Francisco 49ers at the end of the regular season on Sunday.
While in the NFL, Harbaugh led the 49ers to NFC Championship Game in each of his first three seasons and lost Super Bowl XLVII to the Baltimore Ravens, coached by his brother John.
But his final season with the franchise proved to be his poorest, with an 8-8 record only secured on the final day of the campaign thanks to a win over the Arizona Cardinals – he was unsettled by links with a move to Michigan for much of the year as well.
His deal with the Wolverines is reported to be worth $35m over seven years with added performance incentives. They struggled to a 5-7 record last season, only their third losing season since 1967, and that led to the firing of under-fire coach Brady Hoke.
“Throughout my life I have dreamed of coaching at the University of Michigan,” said Harbaugh. “Now I have the honour to live it.
“Across every discipline on campus, the University of Michigan stands for excellence. I feel privileged to take a leadership position at one of the finest universities in the world.
“I truly believe it is time to ask what we can do for our great university, and how I can be a great teammate. I commit to do my part to see to it the Michigan football program upholds its tradition of excellence.”