The coach says the club did everything it could to convince the Argentine to stay but his mind could not be changed, before adding that the German will remain in Madrid.
The Argentine winger has been linked to a move away from the Santiago Bernabeu this summer and is understood to be close to securing a move to Manchester United after telling the European champion he wants to leave.
Ancelotti confirmed the 26-year-old's wish has been granted but would not say where the former Benfica player is going.
"Di Maria has not come here to train, just to say goodbye," he told reporters. "It's not official yet, but everything is being sorted. We thanked him for what he has given the club and we wished him good luck. I have had a very good relationship with Di Maria. He has done a fantastic job at Real Madrid. We are able to replace him very well.
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"It was his decision, because the club did everything possible to keep him, offering everything we could to have him here. He decided otherwise, so good luck to him."
The coach also shed light on the future of Sami Khedira, who has also been the subject of much speculation, saying he will stay in Madrid this season, before adding that the Spanish side will not look to make any more signings this summer.
"With Khedira, it is also solved. Khedira is staying, he is happy to stay and we are happy the issue is clarified," Ancelotti said. "We are well covered. We have many players in midfield."