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.
Notable deaths of 2014 [PHOTOS]