The 26 year old has made 14 appearances for the Potters since joining in January.
Stoke announced Wollscheid has signed a three-year deal after the club paid an undisclosed fee to Leverkusen.
Stoke chief executive Tony Scholes said on the club's website: "We're delighted to have secured Philipp's services on a permanent basis
He joined us midway through the season but wasted little time in making a big impression
"Within days of arriving in England he made his debut against Arsenal at the Emirates Stadium and went on to become an important member of Mark's squad.
"He's clearly enjoying life in England; he feels very settled here and had no hesitation in committing his long-term future to Stoke City."
According to reports, Stoke have paid around £2.75million for the defender, who has been capped twice by Germany
Source : PA
Source: PA