Terms of the deal for Jones were not disclosed by the Jaguars (3-5), who have a bye following Sunday's 24-18 setback to the Philadelphia Eagles at Wembley Stadium in London. The loss was Jacksonville's fourth in a row.
Jones, who recently worked out for the Jaguars, completed 108-of-169 passes for 1,310 yards with eight touchdowns and seven interceptions during his five seasons with the Pittsburgh Steelers. The Jaguars, who return from their bye to face the Indianapolis Colts, play the Steelers in Week 11.
The 29-year-old Jones was released in September by the Steelers, who elected to keep Joshua Dobbs as Ben Roethlisberger's backup.
Bortles has started 69 consecutive games for the Jaguars, who also have Cody Kessler on the roster.
Signed to a three-year, $54 million contract extension in February, Bortles has committed 10 turnovers in eight games this season. The 26-year-old has completed 175-of-290 passes for 2,021 yards with 10 touchdowns and eight interceptions in 2018.
Bortles completed 16-of-22 passes for 175 yards in the first three quarters on Sunday and then connected on just 8-of-19 throws for 111 yards in the last 15 minutes. The 58.5 completion percentage marked the fourth straight game and fifth time this season that Bortles had failed to complete 60 percent of his passes.