The club announced that they had agreed a deal worth £59.7 million (€70m) with the Spanish giants.
That fee eclipses the previous British record of £50m (€62.8m) paid by Chelsea to Liverpool for Fernando Torres in 2011.
Di Maria bid farewell to his Real team-mates on Sunday and flew into Manchester last night ahead of a medical.
The expectation is that the 26-year-old will make his debut for United in Saturday’s Premier League match at Burnley.
United boss Louis van Gaal would neither confirm nor deny anything with regard to the Di Maria situation after his side’s 1-1 league draw at Sunderland on Sunday.
Van Gaal said: “I cannot say anything about transfers, you have to understand that. When a transfer has been finished, then we can say something. But now you have to wait and see.
“When the moment is there, Manchester United shall announce it.”
While Di Maria was putting the finishing touches on his transfer to United, his soon to be former team-mates were beginning theirLa Liga challenge with an unconvincing 2-0 victory over promoted Cordoba.
It took Karim Benzema 30 minutes to find a way past the second division play-off winners with a powerful header and Real toiled in vain for the best part of an hour with the second goal proving to be frustratingly elusive.
Carlo Ancelotti’s men had perhaps been lucky to avoid conceding an equaliser to their plucky opponents at a packed-out and restless Bernabeu, but Cristiano Ronaldo eased the pressure and made the points safe on the stroke of full-time.
Van Gaal, meanwhile, has defended his decision to use Adnan Januzaj as a holding midfielder in the draw at Sunderland, insisting he saw it as the best thing to do at the time to boost their chances of victory.
After Jack Rodwell’s header for the hosts had cancelled out Juan Mata’s opener in the first half of the Premier League contest, Januzaj was brought on in the 63rd minute as a replacement for Darren Fletcher, simultaneous to Danny Welbeck coming on for Robin van Persie up front. Van Gaal opted to put the teenage Belgium winger in the unfamiliar position despite also having the more natural-looking option of Shinji Kagawa at his disposal.
And the manager — who was without the likes of injured midfielders Michael Carrick, Marouane Fellaini, Ander Herrera and Anderson — said: “It is not usual that we have four injuries in midfield. Every club that has that, has a problem.
“That is why I played Januzaj in midfield, [and] because as a coach I want to win.
“I have said that we need creative passing and I thought Januzaj could provide that. That is the reason.”
United’s next match is tonight’s Capital One Cup tie at MK Dons, and Herrera (ankle) will have his condition assessed ahead of the match.
Whether the Spaniard makes it or not, it certainly seems Van Gaal will not be experimenting by giving Kagawa a chance in the holding midfield slot after the damning assessment he made of the Japan international’s previous effort.
The Dutchman said: “Kagawa, I have tried to play him in that position in the United States [in pre-season] and he could not fulfil my wishes and my philosophy.
“We have spoken about that and he is more of a 10. Juan Mata was playing at 10 and I thought I had to change the other players, which is why I chose to bring on Januzaj.
“It is because of creation. Kagawa can also create, but I asked Adnan to play there because of the lack of midfielders.
“When he played in Belgium, he played in midfield so I asked if he could do it for us.
“I said to him, ‘You are on the bench as a midfielder’, because I want him to focus.
“He played there and you could see it’s not so many times that he’s played there. But he did his utmost and I cannot demand more.”