It has been reported that United have spent 80 million pounds (97 million U.S. dollars) on Maguire, making the England international the most expensive defender in history, breaking the record of 75m pounds that Liverpool paid Southampton for Virgil van Dijk in January 2018.
The 26-year-old has agreed a six-year contract at Old Trafford, with the option of a further year.
Maguire, who scored five goals in 76 appearances for Leicester after joining the club from Hull City in 2017, becomes the second most expensive signing in English top-flight history after new team-mate Paul Pogba (89m pounds), and the second most expensive British player after Wales winger Gareth Bale, who joined Real Madrid from Tottenham for 85m pounds in 2013.
A key figure in England's run to the 2018 FIFA World Cup semifinals, Maguire is United manager Ole Gunnar Solskjaer's third signing of the summer, after right-back Aaron Wan-Bissaka and winger Daniel James.
"It's incredible," Maguire said. "A really proud moment for myself, to join such a big club. I'm really looking forward to it and I can't wait to get started now. My first game of last season was at Old Trafford and it's a fixture I've always looked for when I've been playing in the Premier League, Old Trafford away, and it's now my home.
"I tend to get my head down - I've worked hard and done every session and I've played every game for Leicester, so I feel my fitness is there. That was a big part for me to play because, if I ended up getting the move that I wanted, I would have been fit and in contention to play the first game."
United manager Solskjaer said: "Harry is one of the best center-backs in the game today.
"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."