Baghdatis was born in Paramytha, Cyprus, to a Lebanese father, Christos, and a Greek Cypriot mother, Androula. He has two brothers—Petros and Marinos—and a sister, Zena, who was adopted by his family at just six months old. His father, a native Lebanese (Antiochian Greek Christian) who follows Greek Orthodox Christianity, emigrated to Cyprus from Lebanon and owns a clothes shop. He began playing tennis at the age of five with his father and brothers. He enjoys playing and watching football and is a supporter of Apollon Limassol in Cyprus. He trained at the Mouratoglou Tennis Academy in Paris on an Olympic Solidarity Youth Development Programme Scholarship since the age of 14 and learned to speak French.