“Manchester United is one of the most iconic clubs in world football and the chance to come here and play in the Premier League is something I couldn’t turn down,” he said in a statement.
“There is a lot more that I want to achieve in my career and I know I’m joining a squad full of great players who will all have the same determination to win matches and trophies. Having spoken to the manager I can see how much progress has been made over the last few seasons and I now join a group ready to play at the highest level.
“I want to make an impact here and I will give everything to become part of this club’s illustrious history.”
The 28-year-old is United’s third signing of the summer after Ole Gunnar Solskjaer also brought in Jadon Sancho and Tom Heaton.
Varane was in the final year of his contract at Madrid and the club opted to sell him this summer rather than lose him on a free transfer later down the line.
Over the decade he spent at the Bernabeu he made 360 appearances where he won three La Liga titles and four Champions League trophies.
Sources told ESPN that despite this success, he was looking for a new challenge in the Premier League.