Milan announced on Thursday that the Italy international had given the green light to the transfer and he subsequently underwent a medical at San Siro.
The details of the move have now been confirmed, with Milan posting on Twitter: "Mattia Destro arrives from Roma.
"Now officially at Milan, on loan with a right to buy."
Destro had long been linked with a move to Milan after becoming frustrated at a lack of playing time at Stadio Olimpico this season.
The striker has started just eight times in Serie A in 2014-15, scoring five goals.
Speaking shortly after undergoing his medical, Destro spoke of his desire to help Milan return to their prestigious standing in Serie A.
Milan failed to reach the UEFA Champions League for this season and Filippo Inzaghi's men sit 11th with 26 points from 20 matches this term.
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