Ostrogorsky was born in Saint Petersburg, Russian Empire, the son of a secondary school principal and a writer on pedagogical subjects.
[1] After studying various aspects of Byzantinology in Paris (1924–25), Ostrogorsky received his doctorate from the University of Heidelberg (1927) with the dissertation The Rural Tax Community of the Byzantine Empire in the Tenth Century.
Ostrogorsky made the Kingdom of Yugoslavia his permanent home and taught at Belgrade for 40 years until his retirement in 1973, leaving the Chair for Byzantinology to Božidar Ferjančić.
He also supervised the monograph series of the Institute of which the choice items were his own study Pronija (1951) and the multivolume collection of Byzantine Sources for the History of the Nations of Yugoslavia.
Ostrogorsky remained faithful to Belgrade to the very end, although over the years suggestions were made that he take up residence in an American or Soviet center of Byzantine studies.