Destro, who was granted leave by Roma a day prior, underwent a medical at La Madonnina in Milan on Thursday, ahead of an initial loan deal until the end of the season with the option of a permanent transfer.
The 23-year-old Italy international is relishing the opportunity to lead the 18-time Italian champions back to the top, starting against Parma on Sunday.
"It was a wonderful welcome. I am very happy to be here and to be a part of this group," Destro told Milan's official website.
"I have already spoken to coach [Fillipo] Inzaghi, there is a big desire to do well and to show that Milan are a great side, starting as of this Sunday.
"I cannot wait to get out on the pitch and play. The coach will decide my role.
"This is a big occasion for me, I cannot wait to play and get to know everyone. I want to say a big hello to the fans, we will do everything to do really well in the league."
In that time, Destro has scored five goals for Rudi Garcia's championship hopefuls.
