Varane, 28, is one of the most decorated players in world football and has amassed over 19 trophies in his career so far, including four Champions Leagues, three Spanish titles and the 2018 World Cup.
He has represented France 79 times and was part of the recent French squad at the 2020 European Championship.
Raphaël Varane said: “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.
“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.