Aune studied at Wheaton College, the University of Minnesota, and the University of Chicago. He taught at Saint Xavier College and Loyola University Chicago before taking up an appointment at the University of Notre Dame.
Aune is a fellow of the Royal Norwegian Society of Sciences and Letters and of the Norwegian Academy of Science and Letters. In 2006, a Festschrift was published in his honor. The New Testament and Early Christian Literature in Greco-Roman Context: Studies in Honor of David E. Aune included contributions from Peder Borgen, Robert M. Grant, and Margaret M. Mitchell.