Maguire becomes the most expensive defender of all time, with the Red Devils thought to have paid £85 million for his services.
The England international has agreed a six-year deal at Old Trafford and will have the option of a further year.
Maguire made 76 appearances for Leicester and scored five goals since joining them in 2017, but the former Sheffield United and Hull City ace is delighted to make the move to United.
He told his new club's official website: "I am delighted to have signed for this great club. I have thoroughly enjoyed my time at Leicester and would like to thank everyone at the club, and the fans, for their fantastic support over the past two seasons.
"However, when Manchester United come knocking on your door, it is an incredible opportunity.
"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."