Mata has signed a five-year contract and is available for Saturday's game against Norwich.
"Valencia was a big club anyway but I have left to join a bigger club," the 23-year-old winger said. "It is all about the opportunity to win trophies and I have that here."
The Spaniard said Blues boss Andre Villas-Boas convinced him to move.
"He said he wanted Chelsea this season to play more attacking football, and that I would be a big part of that," added Mata.
"Villas-Boas is someone who won almost everything last year [the former Porto boss won the Portuguese league, Europa League and two domestic cups last season] and we are both here with the idea of winning lots this season."Continue reading the main story Andy Brassell,
European football expert
You can argue Mata brings something Chelsea have lacked since Arjen Robben left - a player with real acceleration who can put defenders on the back foot. I do not think it means an end to Chelsea's efforts to sign Luka Modric as, while Mata can play in the centre, I would be very surprised if he did for Chelsea. I would imagine he will play on the right with Florent Malouda on the left. He is creative and has two good feet, although he is predominantly left-footed. Mata is quite a modest and down-to-earth guy and can be a key player for Chelsea for years to come.
Mata, who can play on the wing or centrally, revealed that he could have a versatile role in a Chelsea side that lacked width last season.
"The plan is that I can play on either flank or even in the middle playing in between the lines of midfield and attack, he said.
"I like to keep the ball and use it well, I am an attacking player and above all I like to set up goals and score them also.
"I want to adapt as quickly as possible to my new surroundings, my colleagues and this league, and I would love to win a trophy in my first season.
"If it can be the Premier League then great."
Chelsea and Valencia confirmed that a fee had been agreed on Sunday and while it has not been officially disclosed reports in Spain suggest the Blues are paying £23.5m.
Mata has been at Valencia since 2007 and as captain helped Spain win the Under-21 European Championship in the summer. He was also part of Spain's 2010 World Cup winning squad.
Mata joined Valencia from Real Madrid's youth team. Last season, the 23-year-old midfielder, who is 5ft 7in tall, scored eight goals to help Valencia to a third-place finish in the Primera Liga.
He was also part of Spain's 2010 World Cup-winning squad.