Arteta left Manchester City to become Gunners manager earlier this season.
Cahill told Sky Sports: "Mikel was always a coach, even as a player. He would take in information, he listened, and he would always look for other options. At the same time, he would talk to the players constantly.
"He's a good leader and he's someone I struck a good friendship with because we had a natural understanding on the pitch, just from his movements and the way he crossed the ball. We talked in and outside of training, analysing the teams we'd be coming up against and we analysed ourselves.
"I think him being at Manchester City was fantastic, but this had to happen. He had to fly the nest, and Arsenal is an amazing club. Unfortunately, he didn't join a club that I love in Everton with all the speculation, but at Arsenal he's doing an amazing job."