Stevens, 36, was tapped to replace Doc Rivers, after guiding the Butler Bulldogs to two straight appearances in the NCAA National Championship game in 2010 and 2011.
Celtics President of Basketball Operations Danny Ainge said despite Stevens' youth, he's the right fit to become the storied franchise's 17th head coach.
"His teams always play hard and execute on both ends of the court," Ainge said. "Brad is a coach who has already enjoyed lots of success, and I look forward to working with him towards Banner 18."
Rivers was sent to the Los Angeles Clippers in exchange for an unprotected 2015 first-round draft pick.
The moves will help the Celtics stock up on first-round draft choices and allow Stevens to mold a new identity for the squad.