The Los Angeles Lakers waived Brewer after the two sides agreed to a contract buyout Wednesday.
Brewer, 31, will be joining his former coach with the Florida Gators, Billy Donovan. Brewer was a starter for back-to-back NCAA championship teams at Florida in 2006 and 2007.
An 11-year veteran, Brewer gives the Thunder a versatile wing player to help fortify a roster that lost starting shooting guard Andre Roberson for the season. Roberson suffered a ruptured patellar tendon.
Coach Luke Walton praised Brewer for his professionalism with the Lakers, even after his string of 317 consecutive games -- the NBA's longest active streak at the time -- ended earlier this season.
"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."
Information from ESPN's Adrian Wojnarowski, Ohm Youngmisuk and The Associated Press was used in this report.