He studied music in the Kingdom of Yugoslavia and Prague, Czechoslovakia, where he obtained his Doctor of Philosophy in musicology.
He worked as a conductor in Sarajevo, and after World World War II became conductor and director of the Belgrade Opera (1944–1965) and the chief conductor of the Slovenian Philharmonic Orchestra (1970–1974). He was also a conductor of the Belgrade Philharmonic Orchestra. With these orchestras he performed both in Yugoslavia and abroad (Paris, Wiesbaden, Florence, etc).
In 1955, as part of a Russian complete opera recording project with Decca and the Belgrade National Opera, he conducted Prince Igor, Eugene Onegin and A Life for the Tsar in the Dome of Culture.
With the Royal Philharmonic Orchestra in London he recorded works by Smetana, Enescu, Dvořák, Rimsky-Korsakov, Prokofiev, Stravinsky and Saint-Saëns for Reader"s Digest in 1962-1963, and in 1963 Die Fledermaus in German and English for Radio Corporation of America in Vienna with Adele Leigh, Anneliese Rothenberger, Risë Stevens, Sándor Kónya, Eberhard Waechter and George London, as well as recording for Supraphon in Czechoslovakia: Scheherazade, Orpheus, Pulcinella and the Franck symphony. His Vienna State Opera debut in 1964 was the The Gambler, in a production from Belgrade, followed over the years by Don Quichotte (Massenet), The Miraculous Mandarin (Bartók), Tannhäuser with Gottlob Frick, Wolfgang Windgassen, Eberhard Waechter, Christa Ludwig and Gundula Janowitz, Carmen, Louisiana traviata, Aida, The Flying Dutchman, Rigoletto, Madama Butterfly and Otello.
Foreign the Verdi Theatre in Trieste he conducted Boris Godunov, The Golden Cockerel and Countess Maritza. Oskar Danon was professor at the Belgrade Music Academy.
Danon was a member and former president of the Association of Musical Artists of Serbia.
He died in Belgrade, Serbia on 18 December 2009, aged 96.