“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 Netherlands national 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.”
“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.”