The world cup winning defender arrived the UK two weeks ago but had to undergo a mandatory two weeks of quarantine before he was allowed to go to Manchester United today.
Manchester United, who hope to finalise the signing in the next 24-28 hours, reached an agreement with Real Madrid last month to sign the France defender for a fee believed to be in the region of £41m including add-ons.
Varane, 28, on Tuesday, August 10 started his medical according to a report by Goal.
The centre-back, will become United’s third summer signing following the arrival of England winger Jadon Sancho from Borussia Dortmund for £73m and the free transfer of goalkeeper Tom Heaton.
He made 360 appearances for Real Madrid during a decade-long stay, winning the Champions League and La Liga both three times.