The Lakers announced the move Saturday.
Brown is averaging 7.0 points per game while hitting nearly 58 percent of his shots in four appearances with the Lakers, who reunited him with college teammate Jordan Clarkson in their backcourt.
Brown likely will continue to get minutes with the Lakers in the absence of Nick Young. The Lakers' top scorer has missed 12 straight games and is likely to be out for two more weeks with a small fracture in his left knee.
Brown was the D-League's top scorer at the time of his move to the Lakers, averaging 24.4 points per game. The Oakland, California, native went undrafted last summer out of Missouri.