United confirmed the signing of the Argentina winger on Tuesday after he completed a medical, with the fee eclipsing the previous British transfer record of £50m, which Chelsea paid for Fernando Torres in 2011.
It also exceeds the £37.1m sum United paid for Juan Mata in January.
Di Maria said: "I am absolutely delighted to be joining Manchester United. I have thoroughly enjoyed my time in Spain and there were a lot of clubs interested in me, but United is the only club that I would have left Real Madrid for. Louis van Gaal is a fantastic coach with a proven track record of success and I am impressed by the vision and determination everyone has to get this club back to the top - where it belongs. I now just cannot wait to get started."
The 26-year-old, who cost Real around £28million when they signed him from Benfica in 2010, is regarded as one of the best attacking midfielders in the world.
His signing is a statement of intent from new manager Van Gaal too.
"Angel is a world-class midfielder but most importantly he is a team player. There is no doubting his immense natural talent," he said. "He is a tremendously fast and incisive left-footed player who puts fear into the most accomplished defence. His dribbling skills and his ability to take on and beat opponents are a joy to watch. He is an excellent addition to the team."
The Argentinian won the man of the match award for his role in Real Madrid's victory over Atletico Madrid in the Champions League final last season, and also made the most assists (17) in the Spanish league last season.
The £71m summer signing of James Rodriguez lessened Di Maria's chances of first-team football at the Bernabeu, however, and Madrid decided to cash in on the player, whose value increased following a successful World Cup in Brazil, where he helped Argentina reach the final.
Paris St Germain were the early front runners for Di Maria's signature, but they pulled out of the race to sign the midfielder after failing to agree a fee with the European champions.
It will be interesting to see how Van Gaal attempts to slot Di Maria into his starting XI.
There seems no natural place for Di Maria in the 3-4-1-2 formation Van Gaal has used since he took over at Old Trafford.
The Dutchman has a plethora of options for the No.10 role, so Di Maria could be converted into a striker, or he could be deployed deeper in midfield.
Another alternative is switching United to a 4-3-3 system with Di Maria as one of the front three, with Wayne Rooney, Juan Mata and Robin van Persie - among others - vying for the two remaining places.
United's summer spending total now stands at over £130m following the signing of Di Maria.
Marcos Rojo (£50m), Luke Shaw (£28m) and Ander Herrera (£29m) have already joined the club, and more signings are expected before the transfer window shuts on Monday night.
Daley Blind, Arturo Vidal and Kevin Strootman are understood to be on United's radar.
But the club have reservations over the state of Vidal's right knee, which was operated on in May, and Roma's Strootman is also recovering from a serious knee injury.
Blind, whom Van Gaal knows well from his time with the Dutch national side, has been told he can leave Ajax if United make an acceptable offer.
As of yet, no bid has been made for the Ajax utility man, according to his representative Rob Jansen.
United, though, are not interested in signing Nigel de Jong from AC Milan.
"At this moment Manchester United have not been in touch with me or Ajax about Daley and I'm not sitting here waiting for the call," Jansen said.
A host of departures are also expected before the window shuts.
Up to 12 players could depart, chief among them striker Danny Welbeck.
Marouane Fellaini was expected to leave, but an ankle injury appears to have scuppered his chances of signing for Napoli.
Javier Hernandez, Shinji Kagawa and Anderson are among a long list of names with question marks hanging over their futures.