The composer Enriko Josif was born on May 1, 1924 in Belgrade to a Sephardic Jewish family. His father, Mosha Josif, a merchant by profession, named his son Haim but later changed his name to Enriko. His father liked to listen to the Italian opera singer Enriko Caruso and out of love for his son Haim called him Enriko. Enriko lost his father at young age. His mother, Sofija, was the daughter of Albert Farhi and Kalina Tajtacak.

Enriko studied music composition in the class of Milenko Zivkovic at the Belgrade Academy of Music. He finished these studies in 1954 and later studied composition in Rome for a year (1961-62). For a short time he worked as a teacher in music schools in Belgrade, and in 1957 he was chosen to be an assistant professor of musical composition at the music academy. After the untimely death of Professor Milenko Zivkovic (1964), Enriko took over responsibility for the musical composition courses and he was appointed assistant professor (1965), then associate professor (1970) and finally full professor (1976). He held that position until his retirement in 1989.

Composer Enriko Josif died on March 13, 2003. He is buried in the Jewish cemetery in Belgrade.