The club disclosed no terms when it announced the deal Wednesday.
Brown has appeared in 10 games for the Lakers while playing under two 10-day contracts last month. He has scored 9.4 points per game with 1.7 assists, 1.5 rebounds and 1.0 steals. He scored a career-best 22 points in a win at Philadelphia on Monday.
Brown led the D-League in scoring at the time of his callup to the Lakers.
Brown played alongside Lakers point guard Jordan Clarkson in the backcourt at Missouri last season.