The Red Devils have secured the services of the Netherlands midfielder - who socerd 41 goals over 175 first team appearances for boyhood club Ajax - in a deal which includes a further £5 million in add-ons.
He said: "I cannot begin to explain how incredible an opportunity it is to join a club with such an amazing history.
"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.
"This team has some of the best midfielders in the world and I know that I can learn from them and also bring my own strengths to the group.
"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 will be available to take part in United's opening match against Crystal Palace on September 19, which kicks off the clubs 2020-21 campaign.
Manager Olle Gunnar Solskjaer added: "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."
Meanwhile, Van de Beek will wear the number 34 on his shift as a tribute to his former Ajax teammate Abdelhak Nouri.
Nouri suffered brain damage following a heart attack during a pre-season friendly fixture in 2017.