Milan move for Montolivo and Traore
Montolivo, 27, spent seven years at Fiorentina, where he was club captain, scoring 17 goals in 230 appearances, while 27-year-old Traore, who has joined from AS Nancy, scored 11 goals in 72 games in all competitions for the French Ligue 1 side.
Montolivo has signed a four-year deal, while Traore has joined on a three-year contract.
Milan are rebuilding having last week said goodbye to seasoned campaigners Gennaro Gattuso, Filippo Inzaghi, Gianluca Zambrotta, Alessandro Nesta and Mark van Bommel.
Midfielder Clarence Seedorf has also been linked in the Italian media with a move to Brazilian side Botafogo.
Milan added on their website that Massimo Ambrosini, who signed a one-year contract extension on Wednesday, will keep the captain's armband next season.