Mata tied up his transfer from Valencia on Wednesday, and will be available for Saturday's game against Norwich, having already trained with the squad earlier.
The left winger, 23, said: "Valencia were a big club but I have left to join a bigger club and it is all about the opportunity to win trophies. I would love to win a trophy in my first season. If it can be the Premier League then great.
"Villas-Boas said he wanted Chelsea this season to play more attacking football, and that I would be a big part of that. I can play on either flank or even in the middle in between the lines of midfield and attack. I like to keep the ball and use it well, I am an attacking player and I like to set up goals and score them."