Stevens, 36, becomes the youngest coach in the NBA. He had been at Butler since 2000 and head coach since 2007.
The move was a risky hire, and the odds are against him. Stevens is young, never played in the NBA and did not coach in a major college conference. Several coaches before him have failed to make the transition despite legacies of success coaching college basketball.
Stevens took Butler from a mid-major team to one of the premier programs in college basketball, including two consecutive Cinderella runs to the national title.
He replaces nine-season Celtics coach Rivers, 51, who reportedly left the team because he wanted a more immediate chance of winning. The Celtics will begin rebuilding after trading away Kevin Garnett and Paul Pierce.
The announcement comes two days after Danny Ainge, Celtics president of basketball operations, said that the team was not in a hurry to hire a new coach.
Stevens has been praised for his knowledge of basketball and dynamic and innovative coaching methods.
But history is not on Stevens' side. Charlotte Bobcats coach Mike Dunlap failed to make that transition and was fired after a single season. John Calipari and Rick Pitino, whose teams have won the last two NCAA championships, suffered the same fate during their brief NBA stints.
Stevens has a system for a college team -- but how that will apply in the NBA is dependent on the players themselves. The NBA is known for being a players' league, and egos run high.
Should Stevens find the right balance, he will be able to run the system he has already proven successful at the college level, but if egos get in the way his transition will be more difficult.