The Warriors announced Wednesday that Brown will replace Luke Walton, who left to become the Lakers' coach.
Brown has a 347-216 career record in eight seasons. He took the Cavaliers to the NBA Finals in 2007 and won Coach of the Year in 2008-09 after helping Cleveland win 66 games.
Brown was also an assistant in San Antonio when Kerr played for the Spurs.
Golden State also signed second-round pick Patrick McCaw. McCaw was selected 38th overall by Milwaukee in last month's draft before the Warriors bought his rights for about $2.4 million.