The 21-year-old England striker now has a contract at United until 2023, with the option of a further year.
Rashford, who is locally born, emerged as the first-choice striker for manager Old Gunnar Solskjaer in the closing weeks of last season and is likely to fill that role again next season with Romelu Lukaku potentially leaving United.
Rashford has made 170 appearances for United since breaking into the first team in 2016, and is seen as a key figure in United's rebuild under Solskjaer after last season's disappointing sixth-place finish in the Premier League.
Solskjaer says "Marcus is one of the most talented English players of his generation ... an outstanding player blessed with natural pace and energy."
It continues United's positive offseason after the recent signings of Daniel James and Aaron Wan-Bissaka.