The 29-year-old signed for Milan from Nancy in 2012 but struggled to establish himself at San Siro - spending last season on loan at Kayseri Erciyesspor.
Having made 27 appearances in all competitions for the Super Lig outfit, Traore will again ply his trade in the Turkish top fight next term.
Traore helped Kayseri Erciyesspor avoid relegation with a 14th-place finish last time out but will likely be involved in European football with his new club.
Bursaspor will feature in the UEFA Europa League next season and Traore is hopeful of enjoying a successful time with his new club.
"I'm so glad I came to Bursaspor," he told their 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."
Saponara moved to San Siro in January 2013 after Milan purchased Empoli's share in him.
