The German central defender, 25, signed on loan from Bayer Leverkusen last month.
Wollscheid, who has been capped twice by his country, said: "As soon as I spoke to the manager over Christmas he sold the move to me.
"I had my first contact with him two days before Christmas and I quickly came to the decision.
"It's a massive opportunity for me - Stoke are a very good club."
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