Morse is signing a two-year, $7 million contract with the Jaguars on Monday, Mike Garafolo of NFL Network reports.
Morse was released by the Bills on Wednesday.
Morse is listed as questionable for Sunday's regular-season finale versus the Dolphins due to an illness.
Morse does not carry an injury designation into Sunday's game versus Las Vegas.
Morse has cleared all concussion protocols and is slated to practice fully Thursday, Joe Buscaglia of The Athletic reports.
Morse (concussion) is ruled out for Saturday's game against the Bears, Chris Jenkins of the Bills' official site reports.
Morse has been ruled out for the remainder of Saturday's matchup against the Dolphins after being diagnosed with a concussion.
Morse is being evaluated for a head injury and is listed as questionable to return to Saturday's contest against the Dolphins.
Morse (elbow) was a full participant at practice Monday ahead of Thursday's game at New England, Alaina Getzenberg of ESPN.com reports.
Morse (elbow) is inactive for Thursday's game against the Lions.