Jacksonville Coach Jack Del Rio announced the decision Wednesday.
The matchup will pit two high draft choices against each other. Cam Newton, the No. 1-overall pick in the 2011 draft, is the 0-2 Panthers' starting quarterback. Gabbert was taken 10th in the draft.
Luke McCown started the first two games this season for Jacksonville (1-1), which released last year's starter David Garrard just before the regular season started. McCown completed just 6-of-19 passes for 59 yards and was intercepted four times in a 32-3 loss Sunday to the New York Jets.
Gabbert was inserted into the lineup late in the game and hit 5-of-6 passes for 52 yards.
As a collegian, Gabbert passed for 6,822 yards and 40 touchdowns while building an 18-8 record while a starter at Missouri.