Ole Gunnar Solskjaer has landed his first signature of the summer after chasing several dead ends.
Van de Beek joins for a fee of around £40m from Ajax after he told the club he wanted to leave.
The 23-year-old has spent his entire professional career with the Eredivisie giants, coming up through their famous academy.
He knows the club inside out and Ajax chief Overmars has paid homage to the Dutchman, who was part of the side that reached the Champions League semi-finals in 2019.
He said: "This is a great transfer for Donny, one which he deserves.
"It’s also a compliment to Ajax’s youth academy, where he has played since he was 11.
"Last summer, there was a lot of interest in him but, luckily, we were able to keep him at Ajax for one more year.
"In the months that followed, he proved very valuable to us in both domestic and European competitions.
"He has now been a part of the Ajax first team for almost 5 years. He is ready for this step and we will miss him."
Aston Villa had priced the Englishman at £80m, which left the Red Devils flummoxed and looking at alternatives.
Van de Beek has joined for around half that price while Solskjaer still has other targets in mind.
He is desperate to sign a defender to partner Harry Maguire at the back while a right-winger is also on his wishlist.
Dayot Upamecano is the priority in defence but the Red Devils face huge competition prising him away from RB Leipzig.
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The Frenchman has been attracting several sides this summer after a stellar campaign with the Bundesliga club.
His performances helped the German outfit reach the semi-finals of the Champions League, the furthest they have got in the competition.