Howard reached a five-year deal, starting at $2 million annually, with a base salary of $400,000, according to the school.
"We have found someone with high integrity, great character and a coach who has unbelievable knowledge of the game of basketball," Michigan athletic director Warde Manuel said in a statement. "Juwan has proven himself to be a tremendous leader, a wonderful communicator and a developer of talent. We couldn't have asked for a better role model for the young men in our program. We are excited to welcome back a member of the family to Ann Arbor."
Howard replaces John Beilein, who left the school last week to become the next head coach of the Cleveland Cavaliers. Beilein led the Wolverines program for 12 seasons, which included two trips to the national championship game.
Howard met with Michigan officials earlier in the week. He became the leading candidate after Providence coach Ed Cooley withdrew from consideration and returned to the Friars.
"I am very excited about the opportunity to lead the University of Michigan's storied basketball program," Howard said. "I have been very fortunate to be part of a great championship organization in the Miami Heat for the last nine years -- three as a player and six as a coach. It was always going to take something incredibly special for me to leave Miami; however, I know in my heart this is the right place and the right time.
"As a 'Michigan Man' I know the place our program has in college basketball and I embrace the chance to build onto that history and lead us to championships both in the Big Ten and national level. We will continue to develop young men on the court, in the classroom and in the community that our fan base will continue to be proud of."
Howard, 46, was a member of Michigan's "Fab Five" recruiting class in 1991, along with Chris Webber, Jalen Rose, Ray Jackson and Jimmy King. In three seasons with the Wolverines, he helped guide the team to two national title games and an Elite Eight appearance.
Howard played for 19 seasons in the NBA with eight franchises. After retiring in 2013, he served as an assistant under Heat head coach Erik Spoelstra.