The English club's football director, John Murtough, said Garnacho's "new long-term contract reflects our confidence in him to continue his exciting development under the guidance of Erik and his staff."
He added: "Alejandro has huge potential, and we are all looking forward to working with him to ensure he can fulfil his ambitions here at Manchester United in the coming years."
Garnacho, 18, said he is "relishing the future and can't wait to create more special memories with this group, in front of our amazing supporters."
The Argentine scored four goals and five assists in 31 matches and helped Man United win this year's League Cup (Carabao Cup).
