Club CEO Adriano Galliani compared the signing of Matri to that of prolific striker Filippo Inzaghi. "It reminds me of when we signed Inzaghi in 2001, I hope Alessandro can follow in his footsteps," Galliani told reporters.
Matri, who failed to cement a regular starting place in Antonio Conte's Juve side, was deemed surplus to requirements in Turin following the signings of Carlos Tevez and Fernando Llorente.
However, with Milan striker Giampaolo Pazzini still recovering from knee surgery and the Rossoneri now qualified for the group stage of the UEFA Champions League, coach Massimiliano Allegri stepped up his bid to bring an extra striker on board.
A brief statement on the club's official website confirmed the 29-year-old's arrival on Friday. "A.C. Milan announce the signing of Alessandro Matri from Juventus Football Club," the statement read.
Galliani also confirmed reports that Milan are still pursuing Keisuke Honda of CSKA Moscow and said the Japanese international's arrival could be likely.
He said talks with CSKA were "ongoing" but luring Kaka from Real Madrid would be "more difficult". "It's one or the other," said Galliani. The Brazilian - who has one eye on securing a place in the national team ahead of Brazil's hosting of the 2014 World Cup - issued a come and get me plea on Thursday.
"It would be better for me and the club that I leave," Kaka said. "My father is currently talking to Real, we'll see if we can come to an agreement before Monday."