Financial details of the deal were not disclosed but British media reported that United paid an initial fee of 35 million pounds (47 million dollars) for the 23-year-old.
“I cannot begin to explain how incredible an opportunity it is to join a club with such an amazing history," Van de Beek said in a statement. “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."
Having joined Ajax at the age of 11, Van de Beek scored 41 goals and provided 34 assists in 175 appearances in all competitions and helped them win the Dutch league title in 2018-19.
“Donny has all of the technical attributes needed to perform in this team," United manager Ole Gunnar Solskjaer said. “His ability to see space, time his movements and read the game will really complement the qualities that we have in midfield."
United have also been linked with Borussia Dortmund winger Jadon Sancho but the German club have ruled out the possibility of the 20-year-old England international leaving.
United finished third in the Premier League last season to secure Champions League qualification.
The Premier League season kicks off on Sept. 12 but United, who played in the Europa League semi-finals last month, begin their campaign against Crystal Palace at home on Sept. 19.