Thompson will sign a one-year contract with the Jaguars, Jeremy Fowler of ESPN.com reports.
Thompson is scheduled to become an unrestricted free agent this upcoming offseason, Ryan Homler of NBC Sports Washington reports.
Thompson carried eight times for 34 yards and caught all four of his targets for 18 yards during Sunday's 41-35 loss to the Giants.
Thompson recorded two receptions for 26 yards in Sunday's loss to the Eagles.
Thompson did not log any carries but brought in seven of eight targets for 43 yards in the Redskins' 20-15 loss to the Packers on Sunday.
Thompson (toe) carried three times for 14 yards and caught one of two targets for an additional 15 yards during Sunday's 29-21 win over the Panthers.
Thompson (toe) is active for Sunday's game at Carolina.
Thompson (toe) is listed as questionable for Sunday's game at Carolina, but coach Bill Callahan expects the running back to be active, John Keim of ESPN.com reports.
Thompson (toe) was listed as a limited on Thursday's practice report.
Thompson (toe) was a limited participant in Wednesday's practice.