It remains for the player to undergo a medical examination and agree on personal terms to be an official Manchester United player.
Varane is Manchester United’s third summer signing after Englishman Jadon Sancho from Borussia Dortmund and goalkeeper Tom Heaton on a free transfer.
According to reports, the value of the deal is 35 million pounds, rising to 43 million, with additions.
Varane, 28, moved to Real Madrid in 2011 from Lens, to leave after ten years from the team.
Varane played 360 games with Real Madrid in all competitions, winning the Spanish League 3 times, in addition to 4 European Champions League titles.