Trustees unanimously selected the 59-year-old Leath to replace Jay Gogue, who is retiring.
Leath, who has recently been under fire for his use of university aircraft at Iowa State, begins at Auburn on July 15.
"Dr. Leath is a strategic leader who will work alongside the campus community and alumni to elevate Auburn to the next level in instruction, research and outreach," said a statement by trustee Raymond Harbert, who chaired a 14-member presidential search committee.
Unlike when Gogue was hired, the committee didn't publicly identify any candidates or finalists until Leath was named, prompting criticism from some about a lack of transparency.
"I'm just disappointed that that step was not taken with this search," the Opelika-Auburn News quoted Auburn journalism professor John Carvalho as saying.
Last month, officials in Iowa decided not to file criminal charges against Leath following an investigation into whether he broke the law with his use of school aircraft. The review began after an audit found Leath used university planes for medical appointments in Minnesota, personal flight lessons and trips home to North Carolina. He has now reimbursed the university for the flights.
In his resignation letter, Leath said his time at Iowa State since 2012 was "exciting and rewarding."
"As promised, I am turning over the university to the next President better than I inherited it with records in enrollment, retention rates, graduation rates, job placement numbers, as well as records in research funding, private fundraising and numerous other metrics," he said. "I am proud of the many accomplishments that we achieved in economic development and community engagement."
Before going to Iowa State, Leath spent much of his career in North Carolina, serving as a vice president for research of the University of North Carolina System. He received degrees in plant science and plant pathology from Pennsylvania State University, the University of Delaware and the University of Illinois.
Gogue has been president of Auburn since 2007.
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