Varane on his way to Manchester United after deal agreed in principle
Varane will sign a four-year contract and the Red Devils will pay £34 million plus a potential £8 million in add-ons, BBC Sport's Simon Stone reports.
Varane became one of the game's preeminent center-backs in the Spanish capital, winning 18 trophies - including four Champions League titles and three La Liga crowns - over 360 appearances with Madrid.
Acquired as a relative unknown from RC Lens in 2011, the Frenchman supplanted Pepe in the starting lineup in 2014-15, eventually forming a cohesive partnership with Sergio Ramos.
Madrid allowed Varane to leave with one year remaining on his contract.
The World Cup winner - known for his pace, aerial ability, and sense of calmness - is expected to anchor United's backline alongside Harry Maguire. Victor Lindelof, Maguire's partner for the last two seasons, and Eric Bailly will lose significant minutes as a result.
It's not immediately clear if Madrid manager Carlo Ancelotti will request a replacement for Varane. Though the club signed center-back David Alaba on a free transfer from Bayern Munich earlier in the transfer window, Ancelotti's only other senior options are Eder Militao, Nacho Fernandez, and Jesus Vallejo.
Los Blancos could use the windfall to cover losses from the COVID-19 pandemic. Recent accounts show the club surrendered €300 million in revenue since March 2020.