The 26-year-old Di Maria joined on a five-year contract, taking United's spending to about 130 million pounds ($215 million) in the summer transfer window as England's most successful club seeks to revive its fortunes under new manager Louis van Gaal.
Di Maria was one of Madrid's key players last season when the Spanish team became European champion for a 10th time, but rejected the offer of a new contract and asked to leave.
"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,'' Di Maria said. "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.''
Di Maria's transfer fee breaks the previous British record of 50 million pounds (then $81 million), set in 2011 when Fernando Torres joined Chelsea from Liverpool. Four players Gareth Bale, Cristiano Ronaldo, Luis Suarez and James Rodriguez have cost more than Di Maria in world football, while Zinedine Zidane moved from Juventus to Madrid for a similar fee in 2001.
"Angel is a world-class midfielder but most importantly he is a team player,'' Van Gaal said. "There is no doubting his immense natural talent. He is a tremendously fast and incisive left-footed player who puts fear into the most accomplished defense. His dribbling skills and his ability to beat opponents are a joy to watch. He is an excellent addition to the team.''
The left-footed Di Maria, who can play anywhere across the midfield, will provide United with an injection of pace and technical ability in that area. Both attributes were lacking last season under David Moyes, when the team slumped to a seventh-place finish in the Premier League, and in the first two games of this season under Van Gaal.
It is also a statement by United that the club can attract one of the world's most talented players despite not being in the Champions League or the Europa League this season.
Critics say Van Gaal hasn't addressed the team's biggest weakness a defense that lost three pillars in Rio Ferdinand, Nemanja Vidic and Patrice Evra and has looked vulnerable in a 2-1 home loss to Swansea and a 1-1 draw at Sunderland in the two games so far.
But it is the kind of marquee signing United fans have been craving. The prospect of Di Maria linking up with attacking trio Robin van Persie, Wayne Rooney and Juan Mata is an enticing one.
Di Maria was man of the match in last season's Champions League final against Atletico Madrid and one of Argentina's best players at the World Cup in Brazil until he hurt his thigh in the quarterfinal win over Belgium, forcing him to miss the semifinal and final.