The 20-year old Italian striker spent the second half of last season on loan at QPR but failed to impress and is now planning to produce his best at Old Trafford in what is shaping as a big season for him personally.
"It's great to be back at Manchester United. When you go on loan you really understand how important it is to play for this club," he told the club's official website.
"I'm really happy to be back and I can't wait for the start of the season.
"Last season was disappointing. In the first six months I didn't get a lot of opportunities here so we decided it was best for me to go on loan.
"When I got to QPR things went a bit wrong, though, as I was feeling my ankle a lot. But now I feel a lot better and want to start the season well. It's a big season for me."