The 24-year-old has played overseas with English club Bristol City, and Panathinaikos and Niki Volos in the Greek Super League.
Stambolziev is the Sky Blues' third signing of the January transfer window alongside Senegalese internationals Mickael Tavares and Jacques Faty.
"It's fantastic to be coming home to Australia and signing for the A-League's most prominent club," said Stambolziev.
"I've been here for a short time on trial and I've been able to see the huge amount of quality in this squad."
Coach Graham Arnold welcomed the acquisition of Stambolziev.
"It's great to be able to bring in an attacking Australian player who will add depths to our attacking line up," Arnold said.
Sydney FC resumes its A-League campaign against Central Coast in Gosford on Saturday.
