Leicester have signed Argentina international midfielder Esteban Cambiasso on a one-year contract.
The 29-year-old, whose contract with Cagliari expired this month, has signed a three-year deal with the Rossoneri outfit.
A statement from AC Milan read: "AC Milan announces they have signed Michael Agazzi, who has signed a contract until June 30, 2017."
Agazzi becomes Milan's first reinforcement for next season and his move to the San Siro comes just one day after the club extended veteran goalkeeper Christian Abbiati's contract for a further season.
Agazzi has played on loan at Chievo from Cagliari since the start of the year and made 11 league appearances, helping the Verona outfit retain their Serie A place.
Milan, coached by Clarence Seedorf, finished eighth in Serie A and missed out on European competition next