The official spoke to The Associated Press on condition of anonymity because they were not authorized to release the information.
The university scheduled a news conference for later Monday to announce its choice.
Petrino, 45, is an assistant coach at Arkansas and the younger brother of former Razorbacks coach Bobby Petrino.
He will replace Robb Akey, who was fired at midseason in what ended up as a 1-11 season.
Petrino is the offensive coordinator and quarterbacks coach at Arkansas, where this year he went through the firing of his brother, who was dismissed for hiring his mistress to a position in the athletic department and initially lying about her presence during an April 1 motorcycle accident, and the more recent departure of interim Arkansas coach John L. Smith, a long-time mentor.
Paul Petrino served as an assistant coach at Idaho under Smith from 1992-94, and later coached at Utah State, Illinois, Louisville and with the Atlanta Falcons of the NFL.
He was a standout quarterback at Carroll College in Helena, Mont.
Petrino was one of five finalists for the job at Idaho, which is struggling to remain in the FBS after the Western Athletic Conference dissolved as a football league. The Vandals will play as an independent next year, and are still searching for a conference to join.
Akey was fired in October with the Vandals 1-7 at that point. Assistant coach Jason Gesser was appointed interim head coach and the Vandals lost their final four games. Akey was 20-50 in five-plus seasons as head coach.
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