The deal for the 26-year-old is now subject to a medical.
Maguire was strongly linked with both Manchester clubs over the summer but Leicester held out for their valuation and will receive a world record fee for a defender, eclipsing the £75million Liverpool paid Southampton for Virgil Van Dijk in January 2018.
The deal comes after Maguire was left out of the Leicester squad for their friendly against Serie A club Atalanta at the King Power Stadium on Friday night.
United had made strengthening the centre of their defence a priority at the start of the summer, with the need only becoming more acute when Eric Bailly suffered a knee injury during their pre-season tour of China which is expected to keep him out for at least four months.
The deal represents a tidy profit for Leicester, who signed Maguire for an initial £12million - potentially rising to £17million with add-ons - from Hull in the summer of 2017.
The Foxes were in a strong negotiating position after the Mosborough player signed a new five-year deal in September.