The deal is now subject to a medical and player terms being finalised.
Reports claim United have agreed a deal worth £34m plus add ons to sign the 28-year-old, who was entering the final year of his contract with Real.
The signing represents a massive coup for the Red Devils as Varane - a World Cup and four-time Champions League winner - will now link up in defence with Harry Maguire.
A statement from the Premier League club read: "Manchester United is delighted to announce the club has reached agreement with Real Madrid for the transfer of French international defender and World Cup winner, Raphael Varane, subject to a medical and to player terms being finalised."
Real Madrid also confirmed the deal, stating: "Our club thanks the player for his professionalism and exemplary conduct throughout his ten seasons representing our colours, during which time he has won 18 titles: four Champions Leagues, four Club World Cups, three UEFA Super Cups, three Liga titles, one Copa del Rey and three Spanish Super Cups. "Real Madrid would like to express their gratitude to Varane and his family and wish him the best of luck in this new stage of his career."
4x Club World Cup
3x UEFA Super Cup
1x Copa del Rey
3x Spanish Super Cup#HalaMadridpic.twitter.com/BgQu8WjTTl
— Real Madrid C.F. (@realmadriden) July 27, 2021
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!