The midfielder admits that he was taken by surprise when it became apparent that Milan were after his signature but is eager to prove his worth to the Rossoneri next season.
"I am very happy and very proud to join one of the biggest clubs in the world," he told Nancy's official website.
"I know they attempted to sign me several times and they believe in me. I must now fight to win my place.
"It was strange to hear that they were following me, because I thought I should play in the Champions League to catch the eye of clubs of their size," he said.
Traore plays his last match in a Nancy shirt against Lille on Sunday.
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