He was born as Bogomil Vošnjak in Celje, then part of the Austro-Hungarian Duchy of Styria, in the Slovene branch of the notable Styrian industrialist Vošnjak/Woschnagg family.
Already in May of the same year, he published a book in French, entitled "The Question of Trieste", in which he advocated the unification of the city with a future Yugoslav state.
In 1917, he was among the signers of the Corfu Declaration, a joined political statement of the Yugoslav Committee and the representatives of the Kingdom of Serbia, which was the first step in the creation of Yugoslavia.
In the Assembly, Vošnjak strongly advocated a centralist and monarchist framework of the new country, against most deputies from Slovenia, Croatia and Dalmatia, who favoured federalism.
In February 1921, Vošnjak attacked the Autonomist Declaration, signed by some of the most prominent Slovene liberal and progressive intellectuals, who demanded cultural and political autonomy for Slovenia within Yugoslavia.
During the Nazi German occupation of Serbia between 1941 and 1944, Vošnjak supported the Chetnik underground network of general Draža Mihajlović.