Ćopić was a Bosnian Serb born in the village of Hašani near Bosanska Krupa.He attended schools in Bihać, Banja Luka, Sarajevo and Karlovac before moving to Belgrade to study at the University of Belgrade Faculty of Philosophy until his graduation in 1940.

Upon the uprising in the Bosanska Krajina in 1941, he joined the Partisans and remained in their ranks until the end of World War II. That period of his life influenced much of his literary work as can be seen by the themes he later writes about. At the end of the war he returned to Belgrade where he was, until 1949, the director of a children's magazine called "Pioniri". From 1951 until his death he was a professional writer.

His books have been translated into Albanian, Czech, English, Dutch, Italian, Macedonian, Mandarin, Cantonese, Polish, Romanian, Turkish, Slovak, German, French, and Russian, and some of them have been turned into TV series. He was featured on the 0.50 Bosnia and Herzegovina convertible mark bill, which has been withdrawn from circulation and replaced with coins.

Ćopić committed suicide, jumping off Branko's Bridge in central Belgrade. He is buried in the city's New Cemetery.