The Championship club have embarked on a major recruitment drive this summer, recruiting the likes of Vurnon Anita, Pontus Jansson and Ouasim Bouy as they prepare for a promotion challenge in 2017-18.
Borthwick-Jackson, who has made 14 senior appearances for the Premier League side, becomes Leeds' 11th signing of the summer.
The 20-year-old made his breakthrough at Old Trafford under Louis van Gaal, but has struggled to nail down a first-team spot since the Dutchman's departure.
Borthwick-Jackson subsequently spent last season on loan at Wolves, though he made only seven appearances.
He remains highly-rated, however, and has won caps for England at four youth levels, Under-16, Under-17, Under-19 and Under-20.
Reports suggested that Dutch giants Ajax were keen to secure a deal for the defender, only for Borthwick-Jackson to choose to remain in England instead.