The team and the university made the announcement Wednesday afternoon.
Stevens replaces Doc Rivers, who was acquired by the Los Angeles Clippers.
"Brad and I share a lot of the same values," Celtics president of basketball operations Danny Ainge said. "Though he is young, I see Brad as a great leader who leads with impeccable character and a strong work ethic. His teams always play hard and execute on both ends of the court. Brad is a coach who has already enjoyed lots of success, and I look forward to working with him toward Banner 18."
Stevens, who led Butler to two consecutive appearances in the NCAA championship game, had extended his contract with the Bulldogs through 2021-22.
"Our family is thrilled for the opportunity given to us by the leadership of the Boston Celtics, but it is emotional to leave a place that we have called home for the past 13 years," Stevens said.
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