Ancelotti was presented to the press as Jose Mourinho's successor on Wednesday afternoon, having put pen to paper on a three-year contract with los Blancos.
Perez immediately expressed his delight at having finally managed to get his man, but was just as eager to underline the enormity of the job that Ancelotti has undertaken, warning that lifting the Champions League is the club's top priority.
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"He is a man who possesses great knowledge of the game, an intelligent winner and an extraordinary person.
“Ancelotti is used to the highest pressure of the most intense coaching jobs, but he has to know that nothing he has experienced so far will be like what awaits him at this club
“We are talking about one of the world’s top coaches. As a player, he was a fundamental part of the great AC Milan side.
"But, you know, Carlo, that the Champions League is the most coveted trophy, both for our members and our fans ... "
Perez has no doubt about Ancelotti's ability to deliver exactly what he wants, though, admitting that he has been chasing the former Italy international for some time now.
“Some years ago, Carlo, I said to you: ‘You will be my coach’. That day has arrived.
"Ancelotti’s dream was to coach Real Madrid and now it has become a reality. The challenge starts here, and here the challenges are always huge."
Ancelotti joins Madrid just over a month after leading Paris Saint-Germain to their first Ligue 1 title since 1994.