Petrino will be introduced Thursday morning at a news conference at JQH Arena in Springfield, Rittenberg reports.
He holds a 119-56 career record as head coach at three different schools. He's worked for Louisville (2003-06; 2014-18), Arkansas (2008-11), and Western Kentucky (2013).
Petrino posted a 36-26 record with Louisville in his second tenure at the school and was on the sidelines when quarterback Lamar Jackson won the Heisman Trophy.
The 58-year-old also had a brief campaign as head coach for the Atlanta Falcons in 2007. Petrino resigned from the team amid a 3-10 start to join the Razorbacks at the time.
Missouri State finished last season 1-10, including a seven-game losing streak to close the year. The Bears parted ways with coach Dave Steckel after just 13 wins over five seasons.