The 27-year-old's three-year deal expires next month and the Ligue 1 side had already announced that he would move to the San Siro.
Milan have now made the move official, making Traore the first ever Malian to represent the
Traore was born in Bondy, France, and made 106 appearances for Amiens SC, scoring 15 goals, before making the switch to Nancy in 2009.
At the time of the switch, the midfielder had recently made his international debut for Mali against Angola. He has since earned 21 caps and scored twice.
The arrival follows that of Fiorentina captain Riccardo Montolivo, as the Serie A runners-up begin a rebuilding of their ageing squad.
Alessandro Nesta, Gennaro Gattuso, Filippo Inzaghi and Mark van Bommel have departed the club so far in the close season.