"It's been a wonderful welcome," the 23-year-old told Milan's website after he was met by chief executive Adriano Galliani and they were escorted off the platform by police, amid a crowd of fans, photographers and cameramen.
"I can't wait to get on the pitch and play."
Destro, who still had to face a medical, has scored five goals for Roma this season but relations with coach Rudi Garcia have deteriorated as he has started only eight games.
Milan did not give any details of the deal but Italian media said it would be a loan with an option to buy.
Destro, who has played for Italy at every age level, joined Roma in the 2012 close season from Siena.
He initially found it difficult to get into the team, then injured his left knee in a Coppa Italia match against Inter Milan in January 2013.
It was predicted that he would be out of action for two months and he made a gradual return to the Roma team towards the end of the season.
But after a European under-21 championship match for Italy in Israel in June he suffered a recurrence of his injury, leading to a war of words between the national team and the Serie A side.
He finally returned to action in December 2013, making an instant impact after he came off the bench against Fiorentina to score the winner.
He went on to score 13 league goals in 20 appearances last season and made the provisional list for Italy's World Cup squad, but was cut from the final 23.
(Writing by Brian Homewood in Berne; editing by Toby Davis)
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