Čajkanović studied classical philology at Belgrade's Grandes écoles (Velika škola), and received an international scholarship, on the recommendation of professor Pavle Popović, to take post-graduate studies at the University of Leipzig and University of Munich (where he took his Master of Arts degree) and finished his doctorate under Karl Krumbacher.

In 1908 he became a Latin lecturer at the Belgrade University School of Philosophy and published his MA dissertation, Quaestionum paroemiographicarum capita selecta, in Tübingen.

There he participated in preparing lectures organized by the Serbian Legation and during his free time read and studied at the Bibliothèque Nationale in Paris and the British Museum Library in London.

In the eyes of the Communist regime, "Dr. Veselin Čajkanović, dean at the Faculty of Philosophy of the University of Belgrade during German occupation, represented the university as a member of the Ministry of Education and Faith's Advisory Board on the creation of the Serbian civil plan, whose initiator and organizer was Vladimir Velmar-Janković, assistant of the Minister of Education and Faith."

Above all a professor who was relatively uninterested in politics and causes, Čajkanović certainly realized, as did his compatriots and fellow-professors, Vladimir Velmar-Janković, Slobodan Jovanović, Dimitrije Najdanović, Miloš Mladenović, Djoko Slijepčević and many others, who left the country in time, that an environment of occupation, revolution and civil war was – as Čajkanović put it – "hardly the time for teaching."