Shelton said his leaving was a mutual decision by him and the bowl's board of directors.
Shelton left his post as president of the University of Arizona to take over at the Fiesta Bowl on June 13, 2011.
He replaced John Junker, who resigned following a scathing internal report outlining lavish spending and a scheme in which bowl employees were required to make donations to certain political candidates and have the money reimbursed by the bowl.
Junker is awaiting sentencing after pleading guilty to federal and state charges in connection with the campaign finance scheme.