The Argentinian had signed a six-year deal when he joined Real from Benfica in 2010 but has been rewarded with an enhanced contract after a return of seven goals and 16 assists from midfield last season.
He 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."
The 24-year-old 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. 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."
