The 27-year-old agreed a Bosman transfer to the Rossoneri from Nancy in mid-May, agreeing to a three-year deal once his contract in France wound down to its conclusion this summer.
"I was surprised by the wonderful welcome from everyone. It is a dream come true to play here and now I want to repay that faith on the pitch," Traore told Milan's official website.
"I am a versatile midfielder - I can play in any position in a midfield diamond, from the inside midfielder, further back and playmaker.
"It has been said that Italy is playing a more defensive football, but I disagree - there is much more to me than believed in France, I hope to demonstrate that here and realise my full potential.
"I have been compared to Patrick Vieira as a midfielder, who at Arsenal showed his ability to do well both in defence and attack.
"My teammates who speak French are helping me in these days to understand the drill, but I will soon understand everything myself."