The 22-year-old Germany international is the first signing of Jose Mourinho's second spell in charge at Stamford Bridge having signed a five-year deal in west London.
"Hopefully I can win a lot of titles in the next five years," he told the club's official website.
"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.
"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.
"I'm really looking forward to working with Mourinho. 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.
"He's a very good person with a big personality; he's a great manager so it's an absolute honour for me to now be one of his players."
Schurrle, who can play as a creative wide player or central striker, has scored seven goals in 24 appearances for Germany since making his debut in November 2010 and will wear the No 14 shirt.
He added: "They finished the season very strongly; finishing third was very important for the club, qualifying for the Champions League without having to go through the qualifiers, so the last month in particular was very good."
He believes his best position is on the flank, but it will be intriguing to see how Mourinho sets out a team with Oscar, Juan Mata, Eden Hazard and Kevin de Bruyne among the forward options.
"Wide on the left is my best position because I can cut inside and score goals with my right foot, which I hope to be able to do here, but I am confident playing anywhere offensively," Schurrle said.
"They are all great players, very young with lots of quality. It was my dream to train every day with such talented players so I'm very much looking forward to it."
He is also looking forward to linking up with the likes of Petr Cech, John Terry, Frank Lampard and Ashley Cole.
"I can learn many things from them," he said.
"They've all had long careers and they are legends at Chelsea Football Club.
"I've watched them play since I was a young boy, so it's an honour for me now to be colleagues of theirs at Chelsea."