Born in Wellington, Vercoe received undergraduate degrees in music (1959) and mathematics (1962) from the University of Auckland before emigrating to the United States.
[1] Prior to taking these positions, Vercoe supported his doctoral studies by working as a staff statistician at Michigan; it was in this capacity that first acquired an aptitude for computer programming by learning MAD.
In 1965, he married fellow composer and Michigan graduate student Elizabeth Vercoe; they had two children before divorcing in the early 1990s.
As one of the epoch's few specialists in digital synthesis, he has speculated that he was indirectly recruited by president Jerome Wiesner through colleagues John Harbison and David Epstein because Wiesner harbored musical inclinations (having previously collaborated with Alan Lomax) and sought to establish an electronic music laboratory as an inevitable extension of the institution's mandate.
After a two-year period in which Vercoe designed a real-time digital synthesizer, Wiesner and Edward Fredkin personally procured a PDP-11 for the fledgling research program from Digital Equipment Corporation in the summer of 1973, enabling him to abandon his previous methodology in favor of a streamlined, software-based approach.