The Malian midfielder has confirmed that he will ply his trade at San Siro next season and stressed that he is confident about his chances of making an impression in Italy
The details of the transfer were not released by the 27-year-old, but it is believed that he will join Milan for nothing as his contract with Nancy expires in June.
"I am very proud to have signed for a big club, who have some of the best players in the world," Traore told RMC.
"I hope that this will go well and that this will be a step forward. I am not afraid of the competition.
"Every player that wants to improve must not be afraid. If I am good, I know that I will have my chance, as they told me."
Traore, a Mali international, had also been linked with Newcastle and Olympique de Marseille after establishing himself as a key player at Nancy since he joined the club in 2009.