Nancy have confirmed that the Mali international midfielder will leave the Ligue 1 club on a free transfer in June and will ply his trade at San Siro next season
The Mali international penned a three-year contract with the Rossoneri, who will secure the player on a free transfer when his contract expires in June.
Traore had already announced the move on Tuesday, speaking of his delight to have signed for the Serie A side.
The 27-year-old, who had also been linked with Newcastle and Olympique de Marseille, reached an agreement with Milan in mid-April, but waited for the club to secure their Ligue 1 status before announcing the switch.
Traore has been at Nancy since 2009, when he joined the club from Ligue 2 outfit Amiens.