Harsin led the Red Wolves to the GoDaddy Bowl after a 7-5 season -- including a 5-2 mark in the Sun Belt Conference. He will not coach the team when it faces Ball State on Jan. 5 in Mobile, Ala.
Petersen left Boise State for Washington last week.
Harsin, 36, was co-offensive coordinator at Texas prior to replacing current Auburn coach Gus Malzahn at Arkansas State. He worked at Boise State from 2001 to 2010 and was offensive coordinator for the Broncos from 2006 to 2010 before being hired by Texas three years ago.
He signed a five-year contract with the Red Wolves for $700,000 annually and will have to pay a buyout of at least $1 million. At the time of Harsin's hiring, Arkansas State athletic director Terry Mohajir said it was important to get someone who would remain with the program for more than one season.
The Red Wolves have had three straight one-and-done coaches: Hugh Freeze, Malzahn and Harsin.
It was during Harsin's run as offensive coordinator at Boise State that the Broncos put together their most impressive string of victories and emerged as a BCS contender.
Harsin oversaw an offense led on the field by quarterback Kellen Moore, who won 50 games as a starter to become college football's winningest quarterback. During his five years as offensive coordinator, the Broncos put together a 61-5 record, won two BCS bowls and won at least 12 games in four seasons.
He should also be familiar with many of the Broncos' upperclassmen, including junior quarterback Grant Hedrick, who was recruited by Harsin before leaving for Texas.
The Assocated Press contributed to this report.