The 52-year-old Brown will receive a four-year guaranteed contract, a crucial investment by the Sixers as they embark on an extended overhaul of their roster with a new management team. They've positioned themselves to contend for the No. 1 pick in next year's draft after trading All-Star point guard Jrue Holiday to New Orleans.
Brown joined the Spurs as a player development director in 2002. He has been an assistant on the bench under Gregg Popovich for the last seven seasons.
Brown, who replaces Doug Collins, will become Philadelphia's eighth coach since 2003.
The Sixers were the only team without a coach in place for the 2013-14 season. Thirteen teams have changed coaches since the end of the regular season.
Brown is the second Spurs assistant to accept a head-coaching position this offseason. In May, the Hawks hired Mike Budenholzer.