Pennant admits last season was "very frustrating'' for him, but insists he never wanted to leave Stoke.
Regarding his new contract, he said: "I'm over the moon really. I always wanted to stay here.
"I've enjoyed every minute of my time here, even the downs.
"Obviously with the old manager, things didn't work out, but getting a new contract now shows that I wasn't to blame.
"But that is gone and done and dusted. Here and now we have a new manager in and hopefully we can take the big step forward that all the fans want.
"A big part of me enjoying this club and staying at this club is the fans, who from the day I signed until now have been absolutely fantastic and have been wishing me all the best for the future, either here or elsewhere.''
Stoke chief executive Tony Scholes said: "We have been impressed with Jermaine's determination to prove any doubters wrong.
"He clearly had a difficult time last season, but the Stoke fans love him and he loves them. We believe that at 30 years of age, he still has a lot to offer.
"The one-year contract, which has the option to be extended beyond that, has been structured in a way which should ensure he focuses on his performances on the field.''