The 27-year-old signed a four-year contract and joins the Potters for an undisclosed fee.
Stoke boss Tony Pulis told the club’s official website: “This is a fantastic deal for the football club because Wilson has proved himself to be a top class performer at the highest level.
“He has a considerable amount of international experience and played a prominent part in getting Tottenham into the Champions League only two years ago.
“He has great energy and the qualities to become a driving force in the middle of the park; the type of player our fans will love. We have been looking to strengthen our options in midfield and I am delighted to have him on board.”