Di Maria joined Real from Benfica two years ago and he was already under contract at the Santiago Bernabeu until 2016.
However, after scoring seven goals and providing 16 assists last season, the Argentina international revealed he is delighted to have earned an extension.
The 24-year-old told the club’s official website: “I am completing a dream I had as a child.
“I am very happy here and the extension of the contract gives me the chance to continue at Real Madrid for many years and to keep improving.
“When I arrived they said it wouldn’t be easy to win over the Bernabeu, but thanks to God and with the work and sacrifice I have put in every day and in every match I have won this affection. I feel very supported and loved by the club and the fans.”
Di Maria believes his progression as a player also has a lot to do with the influence of Jose Mourinho and is hoping the Portuguese coach’s impact will continue to make him stronger.
“I have changed a lot in all ways since I arrived here,” he added. “From a football perspective I have improved a lot thanks to Mourinho.
“He asked the club to bring me here when I was at the World Cup and things weren’t going well so a huge part of what I am doing in this moment is thanks to him.
“Hopefully I can continue learning every day. I am still young and I think I can learn a lot here and gain experience.”