Di Maria will train with his new team-mates for the first time this morning following his £59.7million British record transfer to United on Tuesday.
But the Argentina midfielder has made it clear he felt forced out of Real and claims “lies” were told about him – although he also says United are the only club he would have joined.
"My cycle at Real Madrid has come to an end," he wrote. "It's impossible to capture everything I've experienced here in a few lines but I hope this letter communicates what I feel at the moment.
"I had the honour to wear this shirt for four years and I feel nothing but pride for what I went through and achieved with my team-mates.
"Unfortunately, I have to go but I want to make clear that this was never my desire. Like anyone who works, I've always wanted to progress.
"After winning La Decima (tenth Champions League) I went to the World Cup with the hope of receiving a gesture from the board, which never arrived. Many things and many lies were told. Someone may not like me. The only thing I asked for was something fair.
"There are many things that I value and many of them have nothing to do with my salary. I hope to find them at Manchester United, one of the biggest clubs in the world."
After completing his move to United, di Maria 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. “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.”
Speaking after the 4-0 defeat by MK Dons in the Capital One Cup, Van Gaal warned not to expect instant results from the former Real man.
"He has to adapt to our culture, our philosophy, he cannot change (just) like that," Van Gaal said.
"You cannot switch to another system and it works like that. You have to train it, it's a matter of time because the process needs time so we shall see if with Di Maria we have to change the system or not."