The 31-year-old joined from Rennes in 2004 and displaced Carlo Cudicini, who the previous season was voted Chelsea's player of the year, to make his debut in the opening match of Mourinho's tenure against Manchester United.
"Petr came here very, very young and immediately, first game of the season, Chelsea-Man United, clean sheet," said Mourinho, ahead of Saturday's match with Cardiff.
"The book is full of clean sheets and the guy is fantastic. His work ethic is amazing. I think he's a very young goalkeeper."
Mourinho's belief that Cech has years ahead of him as a top-level goalkeeper means he is prepared for a quandary at the end of the campaign.
Belgium goalkeeper Thibault Courtois is currently on his third season-long loan spell at Atletico Madrid and has attracted overtures from Barcelona.
The 21-year-old Courtois joined from Genk on a five-year deal in 2011 and has two years left on his contract come the end of the season.
Mourinho, for now, is relaxed about the upcoming decision.
"In this moment I don't think about it," the Portuguese said.
"It's a good decision. We have the best goalkeeper in the world and the best young goalkeeper in the world.
"I don't think many people disagree with me. If somebody disagrees it will not be by far.
"It's a very good problem. Our goal is safe and financially we are also very safe because their value in the market is the value of the best."
As for the prospect of one of the goalkeepers leaving, Mourinho added: "We control the situation. Not Barcelona. Not Atletico. Not another team that can be interested in one of our goalkeepers.
"We don't have a problem. Teams with a problem are teams without good goalkeepers."
Cech has spent the majority of his Chelsea career behind a defence which has included John Terry, unless the captain has been injured or suspended.
Terry has endured a turbulent time since Mourinho's 2007 departure - the Anton Ferdinand racism row, twice losing the England captaincy, injury and missing a penalty in the 2008 Champions League final - but the Portuguese believes he is nearing a return to his best.
"I never said that I saved his career," Mourinho said.
"I was in Italy, I was in Spain, always with an eye for Chelsea, especially my ex players. I was questioning myself what is happening, why he was not performing.
"It was a question mark for me when I arrived but since the beginning I've found him in very good condition.
"He's recovering his self-esteem, he's recovering the feeling of being an important player for the team, which is a feeling that he lost in the last couple of years.
"That's good for him, that's good for me."
Terry made himself unavailable for England during the Ferdinand affair.
Asked if the centre-back retired from international duty too early, Mourinho said: "That's something personal.
"If I was a football player I think I would wait for the national team to say 'we don't need you any more'. That's just my personal feeling. I would wait.
"For sure he has reasons that push him (to make) that decision."