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The 35-year-old has been without a club since leaving Cardiff City in July after Premier League spells with Southampton, Liverpool and West Brom.
Lambert, who scored three goals in 11 appearances for England, said in a statement: "I have had some ups and downs in my career but to have represented clubs like Southampton, Liverpool and playing for my country in a World Cup were beyond my wildest dreams.
"Playing and scoring for England is probably my proudest professional moment and I will look back at every aspect of how I got there with fond memories."