The full-back penned a four-year contract at Stamford Bridge after joining from Torino in a deal worth a reported £21m.
Zappacosta is already familiar with Chelsea manager Antonio Conte having been selected by the coach for the Italy national team, and the 25-year-old is confident that he can play in the wing-back role.
"I trained with [Conte] for a few weeks when I played for the national team under him and from that small experience I gathered, he was a great manager who is always hungry for victory and wants to improve and progress, which is very good for the players because he can convey that philosophy to us," Zappacosta told the club's official website.
"There are similarities. I used to play in a 3-5-2 under Gian Piero Ventura at Torino and while it wasn't exactly the same, I think I will find it quite easy to settle in and obviously there is time to learn."