Ole Gunnar Solskjaer made the 23-year-old Dutch international his first signing of the summer transfer window in a deal that could rise to 44 million euros ($52 million, £39 million).
Van de Beek, who has signed a five-year contract at Old Trafford with the option of a further season, played 175 times for Ajax, scoring 41 goals.
He played an important role in the club’s run to the Champions League semi-finals in the 2018/19 season.
“I cannot begin to explain how incredible an opportunity it is to join a club with such an amazing history,” he said.
“I would like to thank everyone at Ajax. I grew up there and I will always have a special bond with the club. I am now ready to take the next step in my career and perform at the highest level and there is no higher standard than Manchester United.”
He added: “Having spoken to the manager about his vision for this team, the direction that the club is going in is hugely exciting and I cannot wait to be a part of that.”
Van de Beek came through the ranks at Ajax and has gone on to establish himself in the Dutch team.
Solskjaer said: “Donny has all of the technical attributes needed to perform in this team and has the personality required to succeed at Manchester United.
“His ability to see space, time his movements and read the game will really complement the qualities that we have in midfield and his arrival really strengthens the depth of talent we have in that position.”
Van de Beek’s arrival gives Solskjaer enviable options, with Paul Pogba and January signing Bruno Fernandes among his stable of midfielders.
Ajax’s director of football affairs Marc Overmars wished Van de Beek all the best at Old Trafford.
“This is a great transfer for Donny, one which he deserves,” he said. “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.”
United, who finished third in the Premier League last season, open their campaign at home to Crystal Palace on September 19.
Borussia Dortmund’s England winger Jadon Sancho is reportedly a target for Solskjaer but it is understood that the size of the fee is a sticking point.
