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The Red Devils will pay an additional £5m dependent on appearances and success.
The 24-year-old is understood to have agreed a five-year contract, with an option for a further year.
Agreeing a deal for Mount helps to bolster the options for United boss Erik ten Hag in a key midfield area.
Mount came through the ranks at Chelsea, scoring 27 goals and providing 22 assists in 129 Premier League appearances.
The 24-year-old – a Champions League winner with the Blues in 2021 – has won 36 England caps and started the Euro 2020 final defeat to Italy.
United had made three previous offers for Mount, who is out of contract next summer.
They were keen not to get drawn into a saga and his expected arrival at Old Trafford will represent their first bit of business this summer.
Reports suggested that Chelsea were holding out for £65million, but a compromise has now been reached.