The 29-year-old, who has signed a five-year deal, has just returned from the World Cup, where he captained Belgium to the quarter-finals.
"It's hard to describe just how proud I am to join Manchester United," said Tielemans.
"Signing for such a special club feels incredible. It is the culmination of years of dedication since I first fell in love with football."
Tielemans has spent the past three seasons with Villa, having initially moved to the Premier League to join Leicester in 2019.
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