The 27-year-old has made 18 starts in Serie A for Genoa this season and has agreed a return to the club where he began his career, signing a three-and-a-half-year contract at San Siro.
Antonelli joins Mattia Destro, Suso, Salvatore Bocchetti and Alessio Cerci in arriving at Milan in this window, with Parma defender Gabriel Paletta expected to become the sixth signing.
Paletta was an unused substitute as Parma were beaten 3-1 by Milan on Sunday after Roberto Donadoni revealed a move had been agreed, with the 28-year-old undergoing a medical on Monday.
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