The Clippers offered Winger the job late last week, and the sides have agreed on terms for a multiyear contract.
Winger, an assistant general manager/team counsel for the Thunder, will report to Lawrence Frank, the Clippers' new president of basketball operations.
The Clippers have revamped the franchise's front-office structure in recent weeks, with Doc Rivers returning to full-time coaching duties. The Clippers will also hire former Cleveland Cavaliers executive Trent Redden as an assistant general manager.
Winger, 37, has spent the past seven years with Oklahoma City, working closely with executive vice president/GM Sam Presti. He has developed a reputation as one of the league's most respected young executives.
Winger worked five years with the Cavaliers under ex-GM Danny Ferry before joining the Thunder in 2010.