The 29-year-old has struggled to force his way into the first team at San Siro and has now signed a three-year deal with the Super Lig side
The 29-year-old signed for the Rossoneri 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 flight next term.
Traore helped Kayseri Erciyesspor avoid relegation with a 14th-place finish last time out and is hopeful of enjoying a successful time with his new club, who will take part in the Europa League next term.
"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."
Milan also confirmed on Friday that they have purchased the full economic rights of midfielder Riccardo Saponara from Parma.
Saponara moved to the club in January 2013 after Milan purchased Empoli's share in the player.
After spending the latter half of 2012-13 on loan at Empoli, he returned to San Siro last season but made just seven appearances.