The move allows Brewer, an 11-year veteran, to sign with a playoff team as a free agent.
"It was a pleasure to have Corey on our team," Lakers general manager Rob Pelinka said in a statement. "Corey's professionalism and competitive mindset will leave a positive mark on the Lakers for a long time. We appreciate his time with the team and wish him the best of luck for the remainder of his career."
A reunion with his former college coach Billy Donovan in Oklahoma City is a serious possibility, league sources told ESPN's Adrian Wojnarowski. Brewer will talk to other teams, but the Thunder are an early front-runner, sources said.
Coach Luke Walton praised Brewer for being one of the best teammates the Lakers could have. Brewer served as a valued mentor to the younger Lakers. Earlier this season, he had the longest active consecutive-games-played streak in the NBA snapped at 317 but never complained.
"Whether he is frustrated by his playing time or not, he is on the sideline enjoying the young players," Walton said. "An absolutely great, great teammate."
Brewer is the second valued veteran the Lakers will lose after parting ways with Andrew Bogut last month before guaranteeing his contract for the season.
"You miss having those type [of veterans], for sure," Walton said. "But you hope the young players learn from them and carry that with them."
ESPN's Ohm Youngmisuk contributed to this report.