Belgian international Courtois, 22, has returned to his parent club following a long-term loan spell with La Liga champions Atletico Madrid and will battle with the Czech keeper for the starting role at Stamford Bridge.
Cech, 32, who has been Chelsea's number one for the past decade, is back from the dislocated shoulder he suffered in May and has featured in the pre-season games.
"Petr is working hard, he recovered in almost record time from his surgery and he's ready to fight for his position," Mourinho told Sky Sports television.
"Thibaut has just arrived... as the best young goalkeeper in the world, and they will fight. For me this is a good problem and I've never been afraid of making a decision.
"I prefer to be in this position than not to have good goalkeepers for Chelsea. To have Petr and Thibaut together in the same squad is a good problem for me," said Mourinho.
"This is a club that wants to be strong and have real possibilities to compete for trophies so we need competition in every place."
Courtois has been working with his team mates for the first time this week, having been given extra time off after the World Cup in Brazil.
"I just have to work hard and prove myself in training," said the Belgian. "We have to train hard and work hard together as one team.
"All I can do is play well and then hope the manager chooses me. It's the same for everyone.
"I think I'm an all-round goalkeeper but I know I can improve at everything," added Courtois.
"I am only 22, I'm still young and I'm here to learn a lot off (goalkeeping coach) Christophe Lollichon, Petr Cech and (number three keeper) Mark Schwarzer."
Chelsea finished third in the Premier League last season and were knocked out by Atletico in the semi-finals of the Champions League.
Courtois said he expects the 2012 European champions to be competing on all fronts again this season.
"We have lots of young players and new players that want to develop themselves to become even better players and to win trophies with this club," he explained.
"Chelsea as a club always has the ambition to win as many trophies as possible. Chelsea has a team to be champions in England, to win cups and also to play in the final of the Champions League and win it again.
"Obviously there are a lot of good teams both in the Premier League and the Champions League but I think we should be able to go very far in every competition," said Courtois.
(Writing by Tony Jimenez, editing by Tom Hayward)
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