Clark led Jacksonville State to the Football Championship Subdivision quarterfinals last season, compiling an 11-4 mark in his only season.
He will replace Garrick McGee, who joined Bobby Petrino's staff to run the offense at Louisville. McGee served as Petrino's offensive coordinator at Arkansas.
Clark had spent the previous five seasons as the defensive coordinator at South Alabama, where the Jaguars ranked second in the Sun Belt Conference in total defense in 2012.
UAB went 2-10 last season, ranking 122nd among Football Bowl Subdivision teams in scoring defense as the Blazers gave up an average of 43.8 points a game.
Jacksonville State promoted offensive coordinator John Grass to head coach on Tuesday night, hours after announcing that Clark was leaving.
Grass was offensive coordinator and assistant head coach last season after 17 years as a head coach in the high school ranks.
The 1990 Jacksonville State graduate's offense set 49 school records during the Gamecocks' run to the FCS playoffs.
Jacksonville State had 24 scoring drives of less than one minute. The Gamecocks' 6,637 yards of total offense was 1,755 yards more than the previous record.
The team also scored 528 points, 107 more than the previous mark set in 1991, and produced a Ohio Valley Conference-record 48 rushing touchdowns.
Information from The Associated Press was used in this report.