Di Maria had been linked with a move away from the Santiago Bernabeu during the transfer window as Real considered how many players would have to go to make room in their squad for world-record signing Gareth Bale.
Mesut Ozil was sold to Arsenal on deadline day and Di Maria was also reportedly a target for the Gunners, but a transfer did not materialise and the Argentine is thankful to Ancelotti.
Di Maria, who joined Real from Benfica in 2010, continues to enjoy life in Madrid and hopes to repay the coach for having faith in him.
"Yes, I will be staying at Real Madrid," said Di Maria to Fox Sports Radio.
"I have the confidence of the coach, I am very happy and my family also, which is the most important thing."
Di Maria also spoke about his dream of winning the World Cup with Argentina on Brazilian soil next summer, although he admits it will be a very tough challenge.
He said: "We're taking it step by step but of course, you do sometimes dream about what it would be like to win the World Cup in Brazil which would be one of the nicest things that could happen to any Argentinean.
"Let's just hope that we get there, enjoy a good tournament and have the chance to fight for the trophy.
"But anything can happen - one day, you can wake up on the wrong side of the bed and even though you have some of the best players in the world, it can all go wrong and you find yourself on your way home.
"We have to take each game as it comes, and play it as though it though it were the last."