"We are delighted that he has signed a new contract. He represents the future of the club," said manager Alex Ferguson.
"Last year he had a remarkable season and he is developing all the time. Giuseppe is a fantastic talent and we see a great future ahead."
Rossi, who was born in the United States but has Italian nationality, joined United from Parma in July 2004.
The 19-year-old has started just six senior games for United but has scored four times and is highly thought of by Ferguson, who regards him as the best natural finisher at the club.
Rossi said: "It is great to have extended my contract with the best team in the world. I just hope to keep progressing and developing my career."
The teenager is likely to be given further opportunities at first-team level by United next season, particularly if Dutch striker Ruud Van Nistelrooy is allowed to leave