With a midfield exodus set to take place in the summer, the Rossoneri have acted quickly to bring in replacements for the outgoing duo of Mark van Bommel and Gennaro Gattuso
The Italian had long been linked with a move to the Rossoneri, and head coach Massimiliano Allegri already revealed at the weekend that they had snapped up the 27-year-old.
Montolivo had an expiring contract at Fiorentina, and has signed a deal with AC Milan that will keep him at the San Siro side until June 2016.
The midfielder is a product of the Atalanta youth academy, and joined Fiorentina in the summer of 2005. He had since made over 200 official appearances for the Viola, and will now continue his career at Milan.
Nancy had already confirmed that Traore would leave the club for the Rossoneri earlier this week, but the Serie A giants had yet to make the move official.
The 27-year-old midfielder has signed a contract with Milan until June 2015.
Traore started his professional career with Amiens, before joining Nancy in the summer of 2009. He will be the first player from Mali to wear the Milan jersey.
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