The 19-year-old midfielder, who joined the Academy at the age of nine, made his first-team debut in last December’s Champions League match against Young Boys at Old Trafford.
Savage has agreed a new deal that will keep him at Old Trafford until at least June 2025, with the option to extend for a further year.
The Leicester-born youngster signed his first professional contract in April 2021, at the end of a season in which he had made 23 starts for United’s Under-18s side.
He has represented Wales from Under-17 to Under-19 levels.
Savage has enjoyed a variety of experiences in United's youth teams over the course of 2021/22.