Shelton, 65, who left the presidency of the University of Arizona in 2011 to run the bowl game, will return to Tucson to run the Research Corporation for Science Advancement, a statement issued by the bowl organization said.
Shelton "helped re-establish public trust in an Arizona treasure and led the bowl into the College Football Playoff," the organization said.
Bowl board member Duane Woods will head up the organization until a new executive director is hired to replace Shelton, who was paid nearly a half-million dollars a year.
Shelton became involved in the Fiesta Bowl after his predecessor, John Junker, and other bowl officials were involved in a campaign finance scheme in which staffers were illegally reimbursed for making donations to political candidates, the Tucson Sentinel reported Tuesday.
The scandal led to eight criminal convictions.