Stoke manager Tony Pulis, who revealed that there had been interest from a number of Premier League clubs, told the club's official website: "Seyi is a great acquisition for this football club and I am delighted he chose to join us ahead of several other top-flight clubs.
Chief executive Tony Scholes added: "I'm delighted we've signed a Nigerian international to complement the rest of our squad.''
While Wolves manager Mick McCarthy is sorry to lose the combative midfielder, he is confident the 28-year-old has the ability to succeed in the top flight.
"He's a Premier League player and if he gets the opportunity he'll go on," McCarthy said.
"Everyone I've spoken to, I've said 'take him' because if I was a Premier League manager I'd sign him. He's that good."
And despite the former Brann player making a name for himself with Wanderers, the one time Republic of Ireland coach insists Stoke will see even more from him in the coming season.
"He'll probably be even better in the Premier League than he was in the Championship," added McCarthy.