Leicester were holding out for a bid of £95m for Maguire before agreeing to a compromise. The fee is a world record for a defender, eclipsing the £75m Liverpool paid Southampton for Virgil van Dijk in 2018.
It brings to an end more than two months of negotiations and secures Ole Gunnar Solskjaer's top defensive target. Maguire had feared Leicester were pricing him out of a dream move to Old Trafford but after making it clear to the club and manager Brendan Rodgers he wanted to leave, United have been able to seal a deal.