The 26-year-old England international has penned a six-year contract with the Red Devils with the option of a further season.
Maguire becomes the second most expensive signing in English top flight history behind United teammate Paul Pogba, who was worth £89m.
“When Manchester United come knocking on your door, it is an incredible opportunity,” Maguire said.
He added: “From my conversations with the manager, I am excited about the vision and plans he has for the team.
“It’s clear to see that Ole is building a team to win trophies. I am now looking forward to meeting my new team-mates and getting the season started.”
United boss Ole Gunnar Solskjaer was full of praise for Maguire, rating him as one of the world’s best defenders.
“Harry is one of the best centre-backs in the game today,” Solskjaer said.
“He is a great reader of the game and has a strong presence on the pitch, with the ability to remain calm under pressure.
“He will fit well into this group both on and off the pitch.”