Howard received a five-year deal, starting at $2 million annually, Michigan said.
He replaces John Beilein, who left Michigan last week to become the head coach of the Cleveland Cavaliers. Beilein was with the Wolverines for 12 seasons, leading them to two national championship games.
"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," Howard said in a statement. "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 met with Michigan officials earlier this week, and became the front-runner once Providence's Ed Cooley withdrew from consideration and announced he was returning to the Friars.
Howard, 46, was a member of Michigan's Fab Five recruiting class in 1991, along with Chris Webber, Jalen Rose, Jimmy King and Ray Jackson. During Howard's three seasons in Ann Arbor, he helped lead the Wolverines to two national championship games and an Elite Eight appearance. He averaged 15.3 points and 7.5 rebounds during his Michigan career.
The school later removed the Fab Five's Final Four banners from Crisler Arena as part of self-imposed sanctions that stemmed from one of the NCAA's largest financial scandals. Howard was not implicated in the scandal.
"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. "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."
After Michigan, Howard played for 19 seasons in the NBA, spending time with eight franchises. He won two NBA championships with the Heat, in 2012 and '13, and earned NBA All-Star honors in 1996.
Since retiring in 2013, Howard has been an assistant coach with the Heat under Erik Spoelstra. He interviewed for multiple NBA openings this spring, including those of the Cavaliers, Minnesota Timberwolves and Los Angeles Lakers.
"It was always going to take something incredibly special to for me to leave Miami; however, I know in my heart this is the right place and the right time," Howard said.
Added Spoelstra: "Juwan is an absolute star as a person, player and coach. I feel he is more than ready. He is a terrific leader and mentor, which translates very well to the collegiate level. ... He will forever be a champion and part of the Heat family."
Will Howard be successful as Michigan's coach?
Dan Le Batard and Israel Gutierrez explain why Juwan Howard is a good coaching hire for Michigan.
Howard returned to Michigan and earned his degree in 1997.
Several current and former NBA players backed Howard's hiring at Michigan after news of his interview surfaced earlier this week.
"Talk to me nice. Say it is so!!!? My guy deserves this opportunity. This will only be right," former Heat star Dwyane Wade wrote on Twitter.
After the hiring was made official, Wade tweeted: "Man I'm so pumped!!! Another one!"
LeBron James also applauded Howard before he was officially hired, tweeting: "Man WHAT!!!!?? Absolutely the right choice and i hope it becomes a done deal ASAP!! One of my favorite people I've ever met at the age of 16 and been around since then."
With Howard's agreement, Michigan is now the only current Division I school to have alums coaching both the football (Jim Harbaugh) and men's basketball programs. He also will be the seventh coach in Michigan history to coach at his alma mater, and first since Bill Frieder in the 1980s.
Information from ESPN's Jeff Borzello and the Associated Press was used in this report.