Ian Rapoport of NFL Network reported the deal will be complete Monday.
Kessler, 26, threw for 709 yards and two touchdowns against two interceptions during the 2018 season in Jacksonville. His release leaves the Jaguars without a veteran backup on their roster. None of their three remaining quarterbacks—Gardner Minshew, Tanner Lee and Alex McGough—has thrown an NFL pass.
Kessler will likely compete with Nate Sudfeld for the primary backup position behind Carson Wentz after the Eagles lost Nick Foles to Jacksonville this offseason.
The USC product has appeared in 17 games (12 starts) since being selected by the Cleveland Browns in the third round of the 2016 NFL draft. He's thrown for 2,215 yards and eight touchdowns against five interceptions. Teams are 2-10 in games Kessler has started.
While Kessler is a check-down machine as a passer, there are worse backups around the NFL. It was a bit of a surprise when the Jaguars cut him given Foles' less-than-stellar numbers as a full-time starter.
Sudfeld has thrown just 25 passes in three professional seasons but has completed 20 of those attempts for 156 yards and a touchdown. The Indiana product was the third-string quarterback in Philly last season behind Wentz and Foles.
The Eagles could choose to carry three quarterbacks again in 2019. Wentz has finished each of the last two seasons injured, and he is recovering from a back injury.
The winner of the Kessler-Sudfeld battle would be next in line if Wentz suffers another injury.