Morris and the Razorbacks agreed to a six-year contract worth $3.5 million per year, according to Bo Mattingly of ESPN.
Trey Biddy of HawgSports.com initially reported the news on Tuesday.
The Razorbacks have been scouring the coaching market since firing Bret Bielema on Nov. 24 following a 4-8 season in 2017.
Gus Malzahn, who was a walk-on wide receiver in 1984 and '85 at Arkansas and was an offensive coordinator at the school in 2006, had been connected to the job before he agreed to a seven-year deal to remain head coach at Auburn.
The 49-year-old Morris will be tasked with turning around an Arkansas program that has finished under .500 three times in the past six seasons and hasn't won 10 games in a season since 2011.
Morris successfully rebuilt SMU in his three seasons with the program. The Mustangs were 2-10 in his first season, but in 2017 they went 7-5 to earn a berth in the Frisco Bowl on Dec. 20 against Louisiana Tech.