In the club's first Premier League match of the season - a game they won 3-1 at Burnley - it was the 22-year-old Belgian to get the nod ahead of the man who has scarcely let the team down in a decade.
While suggesting Courtois was now the team's long term first-choice goalkeeper, Mourinho stated he did not want Cech to leave Stamford Bridge.
The Portuguese manager told Sky Sports: "Petr Cech was disappointed but football is sometimes like this, players can often be unhappy and be unhappy with managers. But between the group of players and their mates they have to be supportive.
"I hope he doesn't want to go and I hope he doesn't have offers to go and if he does have offers he refuses to go. I would be delighted to have two of the best goalkeepers in the world in my squad."
Before the match, Mourinho explained his reasoning behind the selection and said: "I don't make decisions for the season, I make decisions for a match.
"Obviously a goalkeeper is not the kind of player you change match after match, you must give a bit of stability, but this is about performances so Thibaut has to know that having a goalkeeper of Petr's level sitting on the bench, it means from him we want a high level of performance.
"Ten years ago I also had a very difficult decision to make when we had (Carlo) Cudicini giving fantastic performances in Chelsea's goal for many years. I had in my hands a 22-year-old goalkeeper I thought could be in Chelsea's goals for years and years and years and this situation is quite similar.
"But Petr is an amazing goalkeeper and the difference between them is 10 years, and we have to think about the future of the club and I made the decision to give the goal to Courtois.
"But I'm so, so comfortable and feel so safe by having these two goalkeepers with us. Petr is a fantastic professional.
"He only knew my decision this morning. He fought hard for his place in pre-season. Obviously he's ready to play. How does he behave? In a professional way, which is what we expect from him because he was always a fantastic professional.
"I hope that he'll fight for his place and he will not sit in a comfortable chair and accept the position. He's a winner and he's a fighter and he will fight for his place."