The 20 year old has inked a five year deal.
City boss Roberto Mancini has been an admirer of the young Italian striker since working with him at the Stadio Giuseppe Meazza.
"I think that Mario is one of the best players of his age in Europe, and I very happy to be working with him again," the manager told City's official website.
"His style of play will suit the Premier League, and because he is still so young there is a big chance for him to improve.
"He is a strong and exciting player, and City fans will enjoy watching him."