The 28-year-old defender has already agreed personal terms with United as he enters the final year of his contract with Real.
After a frustrating week of negotiations between the two clubs, a breakthrough has finally been made.
French outlet Le Parisien reports a deal worth around €45m (£38.5) has been agreed.
It is believed Varane could be unveiled as a United player by the end of the week.
The Les Bleus star will sign a contract with United until 2026.
Varane will join Jadon Sancho as another high-profile signing by United this summer.
The Red Devils parted with £73m to sign the England winger from Borussia Dortmund.
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