Brown appeared in 29 games last season with New York and San Antonio. He has appeared in 403 games for seven different clubs, and was briefly with Washington last season though never appeared in a game.
Brown played for the Los Angeles Lakers when they won NBA titles in 2009 and 2010. He has averaged 7.7 points on 42 percent shooting in his career. He made 33 percent of his attempts from 3-point range.
Brown was drafted by Cleveland in 2006. He also played with Chicago, Charlotte and Phoenix.
Miami now has 16 players under contract, with the start of training camp a month away.