The England defender completed his move to Stamford Bridge last week after lengthy discussions regarding personal terms.
Cahill knows now that his performances will be under greater analysis, but insists he can handle the media attention, both negative and positive.
"I will be under the microscope more now, especially when I make mistakes," he said.
"If people do criticise me here I won't take it to heart, that is for sure. All that will happen if people doubt me now is that I will prove them wrong.
"I am ready for everything that comes with this new challenge."
Cahill could make his debut for Chelsea in the FA Cup against Queens Park Rangers next weekend.