Cahill trained with the Blues for the first time on Tuesday morning after finally completing his £7million transfer from Bolton.
The 26-year-old defender has already struck up an understanding with John Terry and Ashley Cole on the international stage and he is certain playing alongside them at club level will boost not only his chances of sealing a place in the England side but also the country's hopes of a successful summer.
"I am sure that the England manager is happy that there is a possibility we could be playing together but you have to be respectful of the fact that I have to earn my position in this team by working hard in training," Cahill told Chelsea TV.
"Coming to a club like Chelsea, there are top-class, international players all the way through the squad so there is going to be strong competition and it is not going to be easy. I just hope when I get my chance I take it.
"Obviously playing with the English boys here will help our understanding.
"But I am taking nothing for granted. I am coming here to work hard and try to get in the team first of all."
Cahill, who has seven caps, hailed Terry for helping him settle into international football.
"It was fantastic to make my first appearance for England playing alongside someone as experienced as John Terry is and as good as John Terry is," he said.
"It made my job a lot easier and I have played a few times with him now and it has been fantastic.
"We only meet up every now and then with England but it was nice that there are faces here that I know and have spoken to before.
"I knew Daniel (Sturridge) a little bit before he came to Bolton (on loan last season), so when he came there, I got to know him a lot more and I am good friends with him now."
Cahill joined Chelsea after more than a fortnight of wrangling over personal terms.
Reports suggested the player had demanded £100,000-per-week, £30,000 more than the Blues were willing to pay, with the parties eventually shaking hands on a compromise figure of £80,000.
Cahill said: "It was a little bit disappointing when everything is out in the press.
"The stories that I read, I didn't read one that was true.
"Most people will tell you it is hard when you stand on the outside and you have things written about you that aren't very nice, but you have to bite your lip because you want to say, 'No, this is the situation, this is what is happening'.
"The comfort I had was that my friends and family knew the situation and what was going on and the club knew the situation and what was going on and that was enough for me.
"A lot of it was rumours and it was unfortunate that things were in the press, especially things that weren't true.
"I pride myself on just playing football and not coming out and saying much and talking too much, so that was a little bit disappointing but that is football.
"It comes with the job and you just get on with it. Hopefully I can work hard now for Chelsea and put in some good performances."
After agreeing personal terms on Friday, Cahill watched Chelsea's Premier League win against Sunderland on Saturday.
He said: "It was nice when I sat in the stands watching the game on Saturday and the fans saw me and chanted my name.
"It is fantastic when you are wanted at a club first and foremost by the manager and the fans, and it is time for me to try to repay that with working hard and putting in performances that will help Chelsea.
"It is an exciting time in my career and I would just like to get on with it now and focus on doing my best."
Cahill added of manager Andre Villas-Boas: "He has been fantastic. When I did speak to the manager, the impression he had on me was massive.
"Like I said, it is always nice to be wanted by the manager, it gives you confidence when you are coming to a new club and I look forward to working under him, that is for sure."
Meanwhile, Josh McEachran and Patrick van Aanholt sealed their loan moves to Swansea and Vitesse Arnhem, respectively, on Tuesday.
And Chelsea also swooped for young Luton brothers Rio, Cole and Jay Dasilva in separate five-figure transfers on Tuesday afternoon, which could rise to seven figures if the trio progress to the Blues' first team.
Twins Rio and Cole, 12, and older brother Jay, 13, have been part of the Hatters academy since the age of seven and the club's head of youth, Gregg Broughton, told Luton's official website: "I am hesitant to talk about the boys in the collective term because they have all have wonderful unique attributes, but this is a historical deal to see three brothers transferred together.
"Jay is a special talent, a fantastic student of the game whose temperament complements his technical ability. Cole has strong physical attributes and is very comfortable in possession, while Rio is a real livewire, whose ability to play in tight areas has always allowed him to shine.
"Their family has a strong footballing background with older brother Ryan playing as a professional here at Kenilworth Road and father Trevor also a very talented player in the past."
