Di Maria flew into Manchester from Spain on Monday night and successfully underwent a medical before finalising a five-year deal on Tuesday.
The Argentine revealed United were the only club he was willing to leave Madrid for and said he cannot wait to work with Louis van Gaal.
“I am absolutely delighted to be joining Manchester United,” Di Maria told the club’s official website.
“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”.
He also had some nice words for the manager Louis van Gaal and praised the determination of every one at Old Trafford to get the club back to the top where it belongs.
“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.”
Van Gaal praised Di Maria as “a world-class midfielder” but added “most importantly he is a team player”.
“There is no doubting his immense natural talent,” continued the Dutchman.
“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”.
He is likely to make his debut on Saturday against Burnley in the Premier League.
26 year-old, Di Maria began his career at one of the most prolific youth academies in Argentinian football, Rosario Central. In 2007, he moved to Europe to play for Portuguese club Benfica, before signing for Real Madrid in 2010.
The Argentina international has 52 caps for his national team, scoring 10 goals.
The fee paid for the winger, eclipses the £50m Chelsea paid Liverpool for striker Fernando Torres in 2011.
United last broke the British transfer record when they paid Leeds £29.1m for former England defender Rio Ferdinand in 2002.