The Argentine winger is now in his third season in the Spanish capital, and he thinks that Mourinho has given him the drive and confidence to succeed in La Liga.
Di Maria said: "The day he told me to sign I was at the World Cup and I was not doing very well but he kept trying.
"I think most of what I am doing here is thanks to him and I try to repay that with hard work every day.
"As a player I've changed a lot with Mourinho and his work. And as a person. To play for Real is something you dream as a kid. I am very happy with my new contract because I have plenty of years ahead of me."
The 24-year-old has helped Real win La Liga and the Copa del Ray since joining from Benfica in 2010.