The 31-year-old Iceland striker sealed a switch to the Potters on transfer deadline day as manager Tony Pulis added a number of new players to his squad.
Stoke become Gudjohnsen's fourth Premier League club, having had previous spells with Bolton, Chelsea and Tottenham, as well as stints at Barcelona and Monaco.
It is from the French outfit where the cool finisher has departed, and he has penned a permanent one-year contract at the Britannia Stadium, despite initial reports that he had joined on a season-long loan.
Speculation has suggested Stoke may have paid £2million for his services, although the club have not released any details of the transfer.
Pulis told his club's official website: "The fact that Eidur is now our player makes this an even better piece of transfer business for this football club.
"The lad desperately wanted to come back and play in the Premier League and he is eager to make his mark at this level again, so he now has an excellent opportunity to achieve that ambition here and help the club move forward."
Pulis also snapped up Jermaine Pennant and Marc Wilson on Tuesday, as well as bringing Salif Diao back on new terms.
The Stoke boss could hand his new signings debuts in their next game against Aston Villa on Monday, September 13.