The 24-year-old joined Real at the age of 14 and was part of their Champions League-winning squads in 2014 and 2016.
He joined PSG last August for £21m on a five-year deal, but scored just twice in 14 appearances before he was loaned to Spanish club Las Palmas in January for the rest of the season.
“His pedigree speaks for itself,” said Stoke chief executive Tony Scholes.
“He hasn’t had the happiest of periods in his career in Paris but he’s still only a young man and is hungry to make a big impression in the Premier League.
“He will most certainly add to the firepower at our disposal.”
Jese is Stoke’s sixth signing of the transfer window.
Defender Bruno Martins Indi joined on Friday, while the Potters have also signed defender Kurt Zouma on loan from Chelsea, while midfielder Darren Fletcher, defender Josh Tymon and winger Eric Maxim Choupo-Moting all joined on free transfers.
Jese, who was linked with a loan move to Middlesbrough in January, played 63 times for Real, scoring 13 goals.
source: http://www.bbc.com/sport/football/40922444