Cahill's protracted £7million transfer to Stamford Bridge was completed on Monday and the 26-year-old has been included in the squad for Saturday's Premier League clash with Norwich.
The England centre-back admits he struggled in a Bolton team locked in a battle against relegation, but has taken comfort from his international performances.
"My form this season has been bit of a rollercoaster, but overall I've been pleased with the way I've been playing," he said.
"For England I've been really pleased, whereas for Bolton it started dodgily before coming into my own over the last couple of months.
"By joining Chelsea from Bolton I'm jumping from one scale to another scale and hopefully having fantastic players around me will make my job easier.
"I've come from a team that is under a lot of pressure and doesn't have too much of the ball, and I'm not being disrespectful.
"With Chelsea you're in possession and on the front foot all the time. That will help me and you've seen that from me with England.
"It's great to be able to get on the ball and express yourself, whereas sometimes at Bolton we played a little bit more direct."
Cahill, who was linked with Tottenham and Arsenal last summer, revealed he took little convincing to join Chelsea and is excited by the prospect of playing in a team that demands silverware.
"This is a fantastic career move for me," said Cahill, who is reported to have signed a five-and-a-half-year contract.
"You always strive to be at the top of the game and coming to Chelsea has given me that opportunity
"The manager didn't really need to sell the club to me, Chelsea being Chelsea. Every competition they enter they look to win.
"To progress I needed to be at a club where there are such fantastic players who are older and more experienced than me. I can really learn from them.
"My first aim is to work hard in training and then, if given the opportunity, to keep hold of the shirt.
"I'm under no illusions that it will be difficult to break into the team.
"I'm over the moon to be here and now I want to show people what I'm all about.
"I've signed a long contract and I feel my best years are ahead of me.
"I've come here to win trophies and titles and that's exciting."
Cahill has been spoken of as a successor to John Terry at the heart of Chelsea's and England's defence, but he is no hurry to replace his new skipper.
"There's no concern from John's side. It's exciting for me to work with the likes of John, it will only improve my game," he said.
"I've learnt a lot from John playing with England and the partnership has gone well up to now. There's competition between all of us here."
Cahill always knew he would join Chelsea, despite the time taken to finalise a transfer that was reportedly delayed by negotiations over wage demands.
"It was a little bit frustrating, probably because the transfer was more in the public eye than it would normally have been," he said.
"I was never in doubt that it would be sorted in the end. I'm pleased that it's done and now I can enjoy playing football."