Stackhouse, 44, and the Commodores agreed to a six-year contract, sources told ESPN. He replaces Bryce Drew, whom Vanderbilt dismissed as coach after a winless SEC season.
"I am extremely excited to join the Vanderbilt family and build on the incredible accomplishments of its athletics program and men's basketball program," Stackhouse said in a statement. "I look forward to furthering Vanderbilt's unique approach to athletics -- blending a powerhouse competitive spirit with elite academics to holistically develop talented student-athletes and celebrate victories on and off the court.
"I would like to thank Malcolm Turner and Chancellor [Nicholas] Zeppos for giving me this fantastic opportunity to direct the Vanderbilt men's basketball program into its next great era."
Turner, Vanderbilt's new athletic director, had watched Stackhouse closely in Turner's previous job as the president of the NBA's G League.
Stackhouse is the first black head coach for men's basketball at Vanderbilt. The school becomes the only Power Five program with a black athletic director, football coach (Derek Mason) and men's basketball coach.
Besides the six-year deal for Stackhouse, Vanderbilt has pledged to upgrade its financial commitment to the program, including increased assistant coaching salaries and budgets.
Stackhouse's intense coaching style won him significant respect in his two seasons as coach of Raptors 905 in the G League, where he won a title in 2017.
He is an interesting counter to in-state rival Memphis hiring Penny Hardaway, setting the stage for a fascinating regional recruiting battle.
An 18-year NBA veteran, Stackhouse was the G League Coach of the Year in 2017. He spent two years as an NBA assistant, including stops with Toronto and Memphis.
Grizzlies coach J.B. Bickerstaff said Friday that nobody is more deserving than Stackhouse.
"Just watching the work that he's put in, the ability that he has to teach the game," Bickerstaff said. "I think Vanderbilt is going to be fortunate for having him. The guys that he's coaching, to be able to develop them the way that he's capable of, I think they did a great job on that hire."
Mavericks coach Rick Carlisle had Stackhouse in the coach's first season in Detroit in 2001-02 and then in Dallas in 2008-09, and he called this an amazing opportunity. Carlisle said Stackhouse has paid his dues as a coach, overseeing the G League team for the experience as a head coach.
"A lot of guys wouldn't want to do that," Carlisle said. "That showed real humility and respect for the game. I figured that Stack would be an NBA coach at some point. So his decision to go to college is probably a little bit surprising to some. Vanderbilt's an amazing school. He's got an iron will. I'm sure he'll turn it around there."
Information from The Associated Press was used in this report.