"I will miss Steve and his many contributions to the board," Peetz said in a statement posted on a university website Thursday. "But I understand and respect his reasons for leaving."
Garban, who served as board chairman from 2010 through last year, was one of the few trustees to be singled out in a scathing internal investigative report commissioned by the university and released by former FBI Director Louis Freeh last week.
Though Freeh concluded that top Penn State administrators actively conspired for more than a decade to cover up allegations against Sandusky, he also criticized the university's board for failures in oversight.
Sandusky, a former assistant football coach, was convicted last month on 45 counts of child sex abuse.
According to Freeh's report, Garban was one of the few trustees aware in October that Sandusky and two university administrators faced imminent indictment. However, he did not inform his fellow board members, many of whom found out about the arrests nearly a month later through media reports.
Former university president Graham B. Spanier and ex-general counsel Cynthia Baldwin, who were also criticized for not fully keeping the board informed, told Freeh's investigators that they had told Garban, thinking that he would pass along the news to other trustees, the report said.
In the days after Sandusky's arrest, Garban and vice chairman John Surma also drew fire from their board colleagues for their handling of the decision to fire head football coach Joe Paterno.
Under their leadership, the board announced Paterno's termination in a hastily called, nighttime news conference that fueled a student riot in downtown State College.
Both opted later not to seek reelection to their board leadership positions, making way for Peetz and vice chairman Keith E. Masser to take control.
During his tenure on the board, Garban, a 1959 graduate of the university, oversaw Penn State's entrance into the Big Ten, and was instrumental in the development of the Milton S. Hershey Medical Center and the Nittany Lion Inn.
In his letter to Peetz, Garban said he took to heart her call last week that all trustees individually evaluate their continued service on the board.
"I have devoted my entire adult life to Penn State University," he said. "Indeed, it is precisely because of my deep gratitude to and respect for my beloved alma mater that I now step aside."
Contact staff writer Jeremy Roebuck at 267-564-5218, jroebuck@phillynews.com or @jeremyrroebuck on Twitter.
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