He was particularly noted for his memorable film and TV pieces, including movies such as Nevinost bez zaštite, Ko to tamo peva, Balkanski špijun, Život je lep, and Tri karte za Holivud.
Kostić was born in Belgrade, to father Aleksandar and mother Smilja, both French-educated medical doctors and recipients of Legion d'honeur.
After the war, teenager Kostić was caught printing and distributing materials against the Yugoslav communist regime, which landed him in jail with a three-year sentence.
[3] Kostić was married to Vera (née Nikolajević d. 2019) [4] who had equally diverse interests: she was a journalist, ballet dancer and rally driver.
[1] From his relationship to actress Stanislava Staša Pešić he had a son Ivan Ejub Kostić, an Arabist who converted to Islam.