Brown will sign a four-year contract to coach the Sixers, according to SI.com, which reported the agreement earlier.
New general manager Sam Hinkie took quite a while looking for a replacement before choosing Brown, who was part of three NBA title teams with San Antonio. The 52-year-old Brown was an assistant under Gregg Popovich since 2002. He also coached the Australian men's national team from 2009-12, and played a key role in helping Manu Ginobili and Tony Parker develop into All-Stars with the Spurs.
Brown is the franchise's 24th coach and eighth since Larry Brown resigned in 2003.
Brett Brown inherits a team completely rebuilding. Hinkie, who was hired away from Houston, traded All-Star guard Jrue Holiday to New Orleans on draft night for the rights to Kentucky center Nerlens Noel. Hinkie also drafted Syracuse point guard Michael Carter-Williams with the 11th overall pick in the first round.
Collins stepped down after the Sixers went 34-48, a year after advancing to the Eastern Conference semifinals. A season that began with promise after the acquisition of former All-Star center Andrew Bynum unraveled quickly, and Bynum never played a game in a Sixers uniform because of knee problems.
Collins left with one year remaining on his original four-year deal worth $4.5 million. He led the Sixers to the playoffs his first two seasons.
Brown becomes the second Spurs assistant to land a head-coaching job this offseason, joining Mike Budenholzer (Hawks).
Information from The Associated Press was used in this report.