The two sides came to terms on a five-year contract, sources told ESPN's Adrian Wojnarowski.
Cleveland will provide Beilein with his first crack at NBA success after the 66-year-old coach flourished at the high school and college levels.
Beilein helped mold the Wolverines into one of the nation's most consistent college programs, leading them to nine NCAA Tournament appearances in 12 years and two national championship games since 2013.
Michigan had failed to reach the Big Dance in nine consecutive seasons prior to his arrival.
The Detroit Pistons and Orlando Magic both pursued Beilein during their coaching searches last year, but he chose to remain in Ann Arbor.
Following the hiring, Cleveland will now shift its focus to Tuesday's draft lottery, where it owns a 14 percent chance of landing the top overall pick.
The Cavaliers finished their first season sans LeBron James since 2013-14 with a disappointing 19-63 record. The team mutually agreed to part ways with head coach Larry Drew - who was promoted after Tyronne Lue was fired six games into the season - shortly after the campaign concluded.