Eze came through Manchester City's academy and represented England at youth level 13 times before deciding to leave the club after eight years.
The teenager confirmed his departure before Manchester United announced the move on Saturday.
“After eight unforgettable years, I have decided to leave Man City and start a new chapter,” Eze wrote on Instagram.
“I am grateful for the opportunities, challenges and memories that have shaped both my career and me as a person.”
Eze now joins Manchester United, who have recently also recruited another City academy player in Karim Cassim.
The move continues United's efforts to attract young talent from their local rivals, with Eze now beginning a new stage of his development at Old Trafford.