Samardžić was born in Mostar, at the time part of PR Bosnia and Herzegovina, in FPR Yugoslavia. His father Milivoje was an ethnic Montenegrin, and his mother Nada was a Herzegovinian Croat from the Ilići suburb of Mostar. Samardžić's father was a Yugoslav People's Army officer, which meant that the family had to move around a lot. After spending the first seven years of his life in Mostar, young Željko lived and attended school in Nikšić, Igalo and Zadar before eventually returning to Mostar during his teenage years.