The Potters snapped up the midfielder from Blackburn on a four year deal for an initial £3.5 million fee which could eventually rise to £5 million.
Pulis said: "Steven is an outstanding young prospect.
"He has made a big impact in the Premier League since he arrived at Blackburn three years ago and I am sure he will prove to be an excellent addition to our squad. He is the type of player who will endear himself to our supporters.
"We needed to freshen up the squad with new additions and Steven's qualities give us good options in key areas of the team."