The former Liverpool winger left the Potters after they chose not to renew his contract.
Speaking to The Mirror, Pennant said: "I'm looking forward to the new chapter in my life.
"I met with the manager (Mark Hughes) and he was honest with me which I appreciated, I wasn't playing and at 31 now I need to be playing games.
"I'd like to thank the club for the opportunity of a new challenge and would like to thank everyone at Stoke City and the fans for the fantastic support over the last few years."
Pennant had not started a Premier League game for Hughes's side this season.