The Potters had announced earlier this month that, with his contract coming to an end, Pennant would be leaving them this summer.
But the 30-year-old has been handed the chance of a fresh start at the Britannia Stadium after impressing new Stoke manager Mark Hughes, who in May was appointed as successor to Tony Pulis.
Hughes told www.stokecityfc.com: "I've admired Jermaine from afar and there is no question about his ability.
"I am looking to introduce more creativity and attacking options to the side, qualities Jermaine can certainly offer us.
"I had a very positive meeting with him and it's now up to him to show everyone what he is capable of doing."
Former England Under-21 international Pennant initially joined Stoke in August 2010 on a loan deal from Spanish side Real Zaragoza, before making the switch permanent later in the 2010-11 season.
He has made more than 70 appearances for the Potters but after featuring only twice last term - both appearances coming in August - he moved to Wolves for a three-month loan spell.
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."
Pennant arrived at Stoke with a reputation for getting into trouble off the pitch, and in the 2011-12 season he denied reports that he had been fined by the club for twice breaking a curfew ahead of matches.
Then, at the end of that campaign, he was given an eight-week jail sentence, suspended for a year, and was disqualified from driving for three years after he admitted drink-driving.