The Switzerland midfielder was signed from Bayer Leverkusen a fortnight ago.
Xhaka had a past experience as a Premier League captain at Arsenal, before it was taken from him by manager Mikel Arteta after clashing with fans.
Xhaka told safc.com: “It makes me very proud to be captain and hopefully I can show my leadership both on and off the pitch. It’s not easy to be captain - I know how much you need to deal with, but I’m ready.
“I think you grow up a leader, it’s not something you can train. This is what I believe. My role won’t be just on the pitch, it will be off the pitch as well. Everyone who knows me knows exactly what they are getting, and I will make sure everyone is happy and we can move forward.
“You have different types of captains. Off the pitch, I’m a guy who likes to have fun, and on the pitch, I demand a lot because I want to win. I want to win, and I am a winner.
“From the beginning, I had a positive feeling about the Club. I can already see how excited the people are here, and they can’t wait for the game.
“I can guarantee that we will give everything on the pitch. After so many years outside the Premier League, we need to show it on the pitch.”