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Perez denied the suggestion that the Portuguese-born coach was relieved of his duties by the club alone at the media conference where the announcement was made.
"No one has sacked anyone, it has been a mutual agreement," Perez said.
"It is not nice for anyone to have to leave but it is also true that after three years we both decided it was the right moment to break this relationship."
Mourinho's time in charge of the nine-time European champions has been littered with high profile bust-ups with the local media and many of his stellar squad of world class players.
Perez went onto hail his demanding standards throughout his time in charge.
"He is a very demanding coach, with himself and with the rest and this wears you down," he said.
Mourinho joined the Spanish giants in 2010 and signed a four-year contract with them, winning the King's Cup in his first season at the club.
A year ago, Real won their first La Liga title for four years, smashing league records along the way and ending Barcelona's domestic dominance. He became the fourth coach, after Tomislav Ivic, Ernst Happel, and Giovanni Trapattoni, to have won league titles in at least four different countries: Portugal, England, Italy, and Spain.
Mourinho then stated that he was motivated by the challenges ahead at Real Madrid and agreed a two-year contract extension which tied him to the club until 2016.
Perez also confirmed that he had approached Paris St Germain to ask about the availability of Carlo Ancelotti.
Ancelotti was reported as saying that he wants to leave the newly-crowned French league champions, which fueled speculation that he was to join Real, to replace Mourinho, who was already widely rumoured to be on his way out of Spain.
"I have asked the club to leave (PSG) and I am waiting for their answer because I am under contract," confirmed Ancelotti, who also guided PSG to the quarterfinals of the European Champions League.
PSG's president Nasser al Khelaifi confirmed Real's approach, but stated that he has no plans to release Ancelotti.
"They
(Real) came and I discussed it with them. He's got a contract with us
for one more year...for me, he's here next year," Al Khelaifi was reported as saying last week.
Al Khelaifi then went into greater detail late last week, saying that Madrid's interest in Ancelloti was more serious than what was initially anticipated.
"I think he signed a pre-contract with Real Madrid, but I can't imagine Real Madrid will make him sign an agreement or there will be a problem in law," he told Al-Jazeera.
