Cahill completed his £7million move from Bolton last week and will compete with David Luiz for the right to partner Terry at centre-back.
The 26-year-old England defender has been spoken of as Terry's long-term successor, but he is wary of comparing himself to the Chelsea skipper.
"They're massive shoes to fill. I wouldn't look at it as filling his boots," he said.
"If I could go on to have half the career he's had, I'd be happy.
"He's been fantastic for club and country. If you come here thinking you'll be the next John Terry...well they're massive shoes to fill.
"There's no reason why I can't have a fantastic career, if I take my opportunity with Chelsea and continue performing for England.
"But that will be down to me and my performances. If I don't achieve that, there will be no-one to blame but myself."
Cahill believes his career will flourish from playing alongside Terry on a regular basis.
"John reads the game fantastically well and people don't realise how good he is on both sides, it doesn't matter what foot it comes to," he said.
"I can learn from him how to read the game and get in the right positions before the ball has arrived. I can learn how to work my left foot better too."