After attending Newtown State School and The Geelong College, he studied Classics at the University of Melbourne from 1969 to 1976 and was a resident of Queen's College from 1969 to 1971.
In 1977 he returned to the Netherlands, where he obtained his doctorate at the Free University, Amsterdam in 1983. In 1992 David T. Runia was appointed to the Chair of Ancient and Medieval Philosophy at Leiden University. In 2002 he returned to Australia on his appointment as Master of Queen's College at the University of Melbourne, a position he still holds.
He is also Professorial Fellow in the School of Historical Studies in the Faculty of Arts at the University of Melbourne.