Cahill completed his £7million move to Stamford Bridge on Monday and has been included in the squad for Saturday's Barclays Premier League fixture at Norwich.
It marked the end of a protracted transfer saga that was reportedly held up when Chelsea balked at his wage demands.
But the 26-year-old England defender insists his desire to join the Blues was founded on footballing reasons alone.
"It's disappointing when you see things in the press. You bite your lip because I didn't read one report that was correct," he said.
"It was upsetting, but my family and the clubs knew the real situation.
"It was really hard (to accept the perception I was greedy) because that's the perception I got.
"It was difficult to read some of the stories. If it was about wages, I would have waited until the end of the season to make the move.
"But I want to play football at a high level and would never turn down the opportunity to join Chelsea."
Cahill explains the reason for the delay in his transfer - the move was not finalised until three two weeks after a fee had been agreed between Bolton and Chelsea - was simply down to timing.
"The fee was announced really early because it had been agreed so early," he said.
"I'd had no dialogue with Chelsea, but it had come out in the press that a fee had been agreed.
"It took four or five days from that point before we even sat down to speak about the move.
"It took a couple of weeks before I had a meeting to speak with the manager. Two days after that I signed.
"The contract took no longer than any other contract I've signed, even my first one at 16.
"But it felt like that because the negotiations were in the public eye as the fee had been agreed so early.
"There's never been a contract that was sorted out on the first day.
"You say what you want and then you meet halfway, that's how it goes.
"It was just a matter of time, making sure that everything went right. It was a big move so everything had to be perfect.
"Now that I'm here, I'm happy and want to concentrate on my football."
Cahill insists he arrives at Stamford Bridge happy to play ugly, if that is what is required.
"It would be nice to get on the ball and play, but I also want to be that English defender who gets their head in and gets stuck in.
"Sometimes it doesn't have to be pretty and if that's the case I'll make it not pretty."
