Wollscheid has signed a three-year contract with Stoke which will begin on July 1 after his Leverkusen deal expires.
"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," chief executive Tony Scholes told the club's official website.
"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."