Boško Čolak-Antić was born in Kragujevac, Principality of Serbia into an influential Serbian family with a long military tradition; the first son of Colonel Ilya Čolak-Antić commander of the Ibar Army during the Serbo-Turkish war, and Jelena ("née" Matić). Čolak-Antić's maternal grandfather was prominent Liberal politician and philosopher Dimitrije Matić who was President of the National Assembly when Serbia gained independence from the Ottoman Empire. He had a younger brother Vojin Čolak-Antić, a divisional general in the army, and a sister Jovanka married to writer Ilija Vukićević. Čolak-Antić was the great-grandson of famous Vojvoda Čolak-Anta Simeonović, one of the leaders of the First Serbian Uprising of 1804. After graduating from secondary school, he went to study law at the University of Geneva, where, in 1894, he graduated as doctor of law. He returned to Serbia and began his career at the Ministry of Finance before transferring to the Ministry of Foreign Affairs in 1898.