The 31-year-old was on the verge of leaving for Chinese club Jiangsu Suning last year before the deal fell through and he barely featured for Real in their run to the La Liga title when the campaign resumed after the COVID-19 stoppage.
The Brazilian has more to offer United and keeping him is important for the 2020/21 season, regardless of who and how many players come in.
Financial details of the deal were not disclosed but British media reported that United paid an initial fee of 35 million British pounds (60 million USA dollars) for the 23-year-old.
The English team became the Europa League champions with a 2-0 win in Stockholm, Sweden.
'The team he was part of showed the world who we are and what Ajax stand for.
"Like you, we pride ourselves on being one of the best at developing talent and giving young players a shot at the highest level".
Asked about Manchester United's approach in January, Van de Beek told Dutch daily De Telegraaf: "Ajax did not want to sell during the winter window and I was also not in favour of a switch in the middle of the season".
'And where better to do so than in your theatre. 'Please take good care of Donny, and help him dream.
"I would like to thank everyone at Ajax". He will head to Manchester after a Nations League double-header with Poland and Italy.
"Everyone has told me how incredible the Old Trafford atmosphere is and I am looking forward to experiencing that, once it is safe for the fans to return".
He will wear the No.34 at Old Trafford, a tribute to former Ajax team-mate Abdelhak Nouri, who was in a coma for more than two years after suffering a cardiac arrest during a match in 2017.
He said: "I always try and focus only on what I should do and how I should develop to become as good of a football player as possible".
Lightning bounce Bruins from playoffs on Hedman’s 2OT goal
For the Lightning, a win Monday would mean advancing to the Eastern Conference Finals for the fourth time in the last six seasons. Tampa Bay coach Jon Cooper calls them guys who have a little bit of dirt under their fingernails.