The Spain international joined from Barcelona in June and returns to the Premier League after three years in La Liga.
Former Arsenal man Fabregas won the Spanish title and the Copa del Rey while at the Camp Nou but joins a Chelsea side who failed to win a trophy last term.
In recent seasons, Chelsea have won the Premier League, the FA Cup as well as the UEFA Champions League and Europa League, with Fabregas eager to bring silverware back to the club.
"My ambitions? My ambitions are to win absolutely everything," he told Chelsea's official website.
"It was very important for me that the deal was done before the World Cup. I wanted my head free and to know what I was going to do next season and where I was going to be.
"I thought I was at the right age and I believed I wanted a change. I looked at all the offers I had and after speaking to the coach I thought Chelsea was the best decision."
Fabregas is one of a host of big names to leave La Liga for Stamford Bridge - with former Atletico Madrid pair Diego Costa and Filipe Luis also making the move.
The 27-year-old midfielder believes Spain team-mate Costa will prove a real asset during the coming season.
"Diego has been progressing immensely in the last couple of years," Fabregas said.
"He is a real threat in every single game; last season he was playing every three days and he was consistently giving really strong performances.
"He goes behind the defence and he makes the kind of runs players like me really like because it gives you an option to play the killer ball. I think he will do superbly here."
