Rashford’s team-mate Cameron Borthwick-Jackson has also extended his deal until 2020.
It caps a truly remarkable breakthrough season at Old Trafford for Rashford, who scored eight goals in 18 first-team appearances after being handed his debut in the Europa League against FC Midtjylland in February.
“I am delighted to have signed a new contract. I have always been a Manchester United fan, so to be playing in the first team really is a dream come true,” Rashford told the club’s official website.
“I am grateful for having the chance to prove myself. To be able to play football at the biggest club in the world means everything to me and my family.”
Rashford scored 138 seconds into his England debut last Friday at Sunderland’s Stadium of Light and has since been tipped to be included in Roy Hodgson’s final 23-man squad for Euro 2016.
United executive vice-chairman Ed Woodward added: “Marcus is a naturally talented footballer with great potential. He has taken his chances well and has integrated into the first team very quickly.
“I am delighted that Marcus has signed a new contract, he is at the right club to continue his development. He is still very young and we need to be patient but he is developing in the right way and we believe he has a great future ahead of him.”
Borthwick-Jackson has been rewarded with a new deal after breaking into the United first-team last season, and also has the option of extending his contract to 2021.
He made 14 appearances for United and will now form part of Jose Mourinho’s first-team squad, along with Rashford.”I have grown up at United and have enjoyed every minute of being here. Last season was an incredible experience to make my first team debut and a dream come true for myself and my family,” Borthwick-Jackson said.
“I feel it stands me in good stead for continuing my development as a Manchester United player. I will continue to work hard and take advice from the manager and his coaching team to improve with every training session.”
Woodward added: “Cameron is one of a number of young players to come through our academy to make their first team debut last season.
“This is something that our club has always done and promoting the academy and U21 players is something that makes everybody associated with the club very proud.