The 25-year-old began his career with Celta Vigo and played one La Liga game for Real Madrid before moving to Germany with Hoffenheim.
He joined Hanover last year and scored eight goals in 30 Bundesliga games.
"Joselu has an excellent pedigree and is a player we have been tracking for some time," Stoke manager Mark Hughes told the club website.
"He has skills and attributes that are different to what we already have within the squad but will complement the attacking players we already have at our disposal."
Joselu joined fellow Spaniards Marc Muniesa and Bojan Krkic in the Stoke squad.
(Reporting by Ed Osmond; editing by Toby Davis)
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