The Argentine has penned a five-year deal and joins Louis van Gaal's side following four seasons at the Santiago Bernabeu, culminating in a Champions League win last year.
He says he is excited to be moving to United, claiming it is the only club he would have left Madrid for.
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"I am absolutely delighted to be joining Manchester United," he 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.
"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 will be available for the club's trip to Burnley on Saturday.