The Juventus striker deemed surplus to requirements at the Bianconeri has rejoined the Rossoneri in a deal believed to be around 11 million euros
Matri, 29, is believed to have signed on a four-year deal at Milan, the side he played for as a youngster before having spells at Cagliari and Juventus, in a deal reportedly worth 11 million euros.
The striker has fell down the pecking order at the Bianconeri, with other attackers Fernando Llorente and Carlos Tevez joining Antonio Conte's men earlier this summer.
But, with the Rossoneri securing its place in the Champions League proper, having seen off the challenge of PSV and Giampaolo Pazzini's return still to be confirmed, coach Massimiliano Allegri has bolstered his squad with the capture of the forward.
Matri made 83 appearances for Juventus, scoring 29 goals.
Meanwhile, a player leaving the San Siro is Kevin-Prince Boateng, who completed his move to Bundesliga club Schalke on Friday.