Ćorović finished primary school and the Gymnasium in Mostar, in which he was one of many future Serb intellectuals, among whom was also his brother the novelist Svetozar Ćorović. Ćorović continued his studies at the University of Vienna in 1904, studying Slavic Archaeology, History and Philology. He was active in the Serbian academic group „Zora“. Ćorović gained a Ph.D. in 1908 with a thesis on Lukijan Mušicki, a Serbian poet from 18th century. His professors at Vienna were Vatroslav Jagić, Konstantin Jireček, and Milan Rešetar. Ćorović was to receive a golden ring from the University of Vienna as one of the top students. He refused to accept the award on account of Bosnian Crisis. In 1908 Ćorović went to Munich for specialized studies in Byzantine history and philology with Professor Karl Krumbacher.