The signing of 31-year-old Gudjohnsen was sealed on a busy deadline day when he the striker flew into England for talks with City after an agreement had been reached with Monaco to mark his return to the Premier League.
Gudjohnsen welcomed the chance to return to England's Top Flight where he had successful spells with Bolton Wanderers and Chelsea, as well as a loan spell at Tottenham last season when he made a big contribution to their win at the Britannia Stadium.
"This is a fantastic signing for the Football Club because Eidur is a player of outstanding international calibre who has performed at the highest level," Stoke manager Tony Pulis was quoted as saying on the Stoke City official website.
"There is no better example of the quality he provides than his contribution to Tottenham's win here in April. Not only did he score an excellent goal, he showed what a great footballing brain he has and his sense of awareness with a key role in their winner.
"Eidur made a significant contribution to Spurs qualifying for the Champions League and I am confident he can have a big impact upon our season.
"He certainly brings more goals to the squad, following the arrivals of Kenwyne Jones and Jon Walters, which was an important aim in this transfer window and I am delighted we have brought these three players in, together with Marc Wilson."Marc Wilson will be one of Gudjonsen's new teammates this season after his capture from Portsmouth. The 23-year-old defender was secured in a player-plus-cash exchange deal which sees Liam Lawrence and Dave Kitson move in the opposite direction.
However, Stoke's signing of Jermaine Pennant was perhaps manager Tony Pulis' biggest last-minute transfer surprise. The former Liverpool winger has been acquired on a loan deal from Real Zaragoza until January 2011.