The 34-year-old, who left AEK Athens in the summer, had been expected to join Seattle Sounders in the MLS. However, he has agreed to join Belgium's bottom-placed club.
"This is not a financial decision, but a lifestyle choice. Many people think it is strange that I am joining Cercle because the contrast with the clubs I have played for in the past is huge," Gudjohnsen told Het Nieuws Laatste.
"But when you know where I am coming from, it is not strange. It's less than a year since I suffered a double fracture."
Gudjohnsen has also played for Barcelona and Fulham.