The 31-year-old Frenchman, who was released by Blues when his contract expired at the end of June, has opted for a move to Greece in preference to signing for League One side Peterborough United with whom he had a spell on trial earlier this month.
"Panionios offered him a great deal, but Franck said he enjoyed his time with us and that he definitely would have come to us if they hadn't come in late and fast for him," Posh manager Gary Johnson told the Peterborough Evening Telegraph.
Queudrue joined Blues from Fulham in August 2007 and was voted the fans' player of the season for 2008-09. He struggled with injuries during his final season at St Andrews and spent the final few months of the season on loan at Colchester United.