Cahill won the Premier League title with Conte at Chelsea.
He told the Daily Mail: "He was a great manager. Conte said, 'Right, I'm changing this'. He knows that formation inside out, and there was not one player on the pitch who did not know his role inside out. If you didn't know it, you didn't play.
"I played left of the three, whereas when we'd won the league with Jose (Mourinho), Azpi (Cesar Azpilicueta) was left back and I was right-sided centre back. Yet then Azpi went from left back to right-sided centre back and I went to the left-sided centre back.
"I spoke to Conte and he was adamant it would work. The Joses, the Contes. The attention to detail, the way they think. They never switch off. You have that confidence; an arrogance in a good way."