The Jaguars sent a 2020 fifth-round draft pick to the Steelers in exchange for Dobbs, according to the team.
Jacksonville's trade for Dobbs comes one day after starting quarterback Nick Foles suffered a broken clavicle against the Kansas City Chiefs. The team placed Foles on injured reserve, creating a need for an additional signal-caller.
Dobbs is expected to be the backup to Gardner Minshew, the Jaguars' sixth-round pick in this year's NFL Draft. Minshew replaced Foles on Sunday and completed 22-of-25 passes for 275 yards and two touchdowns.
The Steelers selected Dobbs in the fourth round of the 2017 draft out of Tennessee. Dobbs didn't play as a rookie but had five appearances last season, completing 6-of-12 passes for 43 yards and an interception.
Foles was scheduled to undergo surgery to repair his broken clavicle Monday. It remains unclear how long he is expected to sit out.