The Italian champions have long been linked with a striker due to Antonio Cassano's illness, and have now moved for the 21 year old after the club gave up on any hope of signing Carlos Tevez.
Roggia, who has an Italian passport, played against Massimiliano Allegri's side in the Audi Cup, a pre-season tournament.
Meanwhile, another player to have joined the San Siro club is Kingsley Umunegbu, who has signed from Swiss side Chiasso.
The Nigerian had previously represented AC Milan in a Coppa Italia match in 2007, but was soon farmed out on loan to a host of Italian clubs, before moving to Chiasso.
AC Milan previously clinched the loan signing of Sulley Muntari from city rivals Inter.
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