The 31 year-old has signed an 18 month deal with the Potters after completing a medical this morning.
The attacking midfielder is the eldest son of former City boss Gudjon Thordarson and his brother Bjarni Gudjonsson, now at Plymouth Argyle, made over one hundred appearances for the Potters in his three years at the club.
Thordur goes straight into manager Tony Pulis' squad (number 33) and could be debut as early as next weekend's game away at Wigan Athletic.
Confirming the news Director of Football John Rudge said: "We're delighted to announce that Thordur has signed an 18 month contract for Stoke City.
"He's got a wealth of experience having played over fifty times at international level and we're pleased to have attracted a player like him to Stoke City.
"Thordur will be a great asset to this football club and myself and Tony Pulis are delighted he has joined us."