Arkansas Director of Athletics Jeff Long said Smith, 63, had inked a 10-month contract worth $850,000, which could go higher with performance and academic achievement incentives.
Smith has been the Razorbacks' special teams coach for three years and took the head coaching job after having agreed previously to lead his alma mater of Weber State.
"Coach Smith brings a wealth of football knowledge, BCS conference head coaching experience, passion for the game and a close familiarity with the current team and coaching staff," Long said.
The Arkansas position became available when Petrino was fired after revelations emerged following an April 1 motorcycle collision of an extramarital affair with a female athletics department staffer, who was also involved in the crash.
"Throughout the spring, the assistant coaches and student-athletes have shown incredible focus and character, which we will use to build on as we work to achieve our goals for 2012," Smith said.