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.
"We want to stay FBS," he said, and the best way to do that is to win games and make themselves attractive to a conference.
He was not ready to announce any of his staff.
Petrino declined to place a timeline on winning.
"We will look at getting better every day," he said. "Your goal has got to be a quick goal. I see guys getting fired after one year now."
Akey was fired in October with the Vandals 1-7 at that point. 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.
Petrino said his father, Bob, his brother, Bobby, and Smith were the three main football influences in his life.
He noted that his brother taught him a lot about football.
"He still is the most brilliant coach in football," he said of Bobby. "He taught me so much about football, paying attention to every detail."