The 29-year-old joined Milan from Nancy in 2012, but failed to settle in Serie A and has now sought pastures new.
"I'm so glad I came to Bursaspor," he told the club's official website. "I will use all my strengths to help bring success to Bursaspor.
"Bursaspor previously had the championship and I am here to repeat that. This past season, I saw how passionate the fans are. They impressed me a lot."
Traore spent last season on loan in the Turkish top flight with Kayseri Erciyesspor.