He studied law, architecture and philology at the University of Belgrade, only to discover acting as his true calling. After graduating at Drama Arts Academy he joined Beogradsko dramsko pozoriste (Belgrade Drama Theatre). In 1968 he joined Atelje 212 Theatre, where he became famous for his role of Kralj Ibi (King Ubu), during which he showed great improvisational ability.

He preferred theatre to film and television, but he nevertheless managed to give memorable performances. International audiences know him best for his role in 1971 cult film WR: Mysteries of the Organism. Audiences in former Yugoslavia know him best for his roles of Bili Piton in 1982 cult comedy The Marathon Family and Radovan Treći in Dušan Kovačević's play with the same name Radovan Treći (Radovan III).
Radmilović's statue in his hometown Zaječar got erected in April 2008.

One of his last roles was in 1985 film When Father Was Away on Business, in which he appeared together with Slobodan Aligrudić. He died shortly after the film won Palme d'Or at the Cannes Film Festival, and Aligrudić died shortly after him, leading many film critics of former Yugoslavia to state that "heaven had received a huge boost".