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The Guinea international made 20 Serie A appearances for Milan last season and becomes one of new coach Vahid Halilhodzic's first signings since taking the reins last month.
Trabzonspor had previously announced they were in negotiations over a move for the player, and confirmed the acquisition with a short statement on their official website on Tuesday.
No details have yet been released about the 27-year-old's contract.
Constant's last appearance for Milan came in a 2-0 friendly victory over Monza on July 20, in which he played 81 minutes.
