The 22-year-old Germany international completed his move to Stamford Bridge from Bayer Leverkusen on Tuesday, and believes the club can challenge for multiple honours
The Portuguese manager left Real Madrid to return to the Blues at the start of June, and Schurrle has become the first signing of Mourinho's second reign at the club.
The 22-year-old, who spent two seasons at Bayer Leverkusen before making the 21 million euro switch to Chelsea, believes Mourinho is one of the best managers in the world and is confident the club can achieve success under him.
“Yes, of course [we can challenge for the Premier League title and Champions League],” Schurrle told the club's official website. “I think we have a great team with some very talented young players. We can all improve ourselves, and under Jose Mourinho I'm confident we can have a really great season.
“He's a very good person with a big personality; he's a great manager so it's an absolute honor for me to now be one of his players.
“I'm really looking forward to working with him. I got to know him at Michael Ballack's testimonial a few weeks ago where we talked a little bit. He gave me advice on where to live and also explained what he expects from me.”
Schurrle does not fear the competition he faces in the shape of Oscar, Juan Mata and Eden Hazard, and believes that quality and rivalry for places can help the club win trophies next season.
“Of course, they are all great players, very young with lots of quality,” the Germany international continued. “It was my dream to train every day with such talented players so I'm very much looking forward to it.
“For this club, winning titles is always the main objective. We have a great young team with so much quality. We are capable of doing well in the Premier League, Champions League and the cup competitions as well, and I hope to play a big part.”