The Red Devils have agreed an initial £34million fee for the Real Madrid defender, who is vastly experienced at the highest level and will bring a wealth of experience to Old Trafford.
United have failed in their efforts to recruit Varane in past windows, but have sent out a strong message to the rest of the Premier League by reaching an agreement to sign the 28-year-old.
Varane notably won three league titles and the Champions League on four occasions during his stay with Madrid and Solskjaer believes this is a deal that highlights the club’s “ambition”.
“Of course, very happy that we’ve managed to get a deal with Real Madrid. Medical should hopefully be OK. He’s a proven winner, a player we’ve followed for many years,” said the United boss.
He added: “First of all the club shows ambition with one of the most exciting young players in world football, then one of the most respected centre-backs. We have different ways of playing with Raphael. I can’t wait to get him in, hopefully we can get that sorted as soon as.
“We’ve scrambled before towards the end of the window and now I have to say we’re in a good position.”
It has been a strong start to the transfer window for the Red Devils, who have already completed a £72.9m deal for Borussia Dortmund winger Jadon Sancho.
United are now being tipped to challenge for the Premier League title as Solskjaer prepares to field a much-improved side to the one he first inherited.
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A new midfielder could also be on the agenda in the transfer window, though this will largely depend on the future of Paul Pogba.
The Frenchman has turned down a new contract at the club and will have to be sold this summer to ensure the club don’t lose him for free next year.
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