United have also moved to tie up the long-term future of a fellow academy graduate Cameron Borthwick-Jackson, who has penned a similar deal.
Rashford's new agreement also includes an option to extend for a further year.
"I am delighted to have signed a new contract," the England international told manutd.com.
"I have always been a Manchester United fan so to be playing in the first team really is a dream come true
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 burst onto the first-team scene in February, scoring twice on his debut in the Europa League against Midtjylland.
The teenager repeated the feat three days later on his first Premier League appearance against Arsenal and went on to score eight goals in 18 appearances.
Rashford also scored within three minutes of his senior England debut in a friendly against Australia on Friday to enhance his chances of going to Euro 2016.
United executive vice-chairman Ed Woodward praised the youngster and the progress he has made.
"Marcus is a naturally talented footballer with great potential," he said.
"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."
Source : PA
Source: PA