The veteran tight end posted a picture on Instagram on Thursday of him signing a contract. He had been in Green Bay visiting the Packers.
The team has yet to announce the move.
Lewis will join fellow free-agent acquisition Jimmy Graham in Green Bay, and it marks the second straight offseason that the Packers have signed multiple tight ends. Last spring, they signed Martellus Bennett and Lance Kendrick on back-to-back days early in free agency.
Bennett lasted only seven games, while Kendrick caught only 18 passes for 203 yards and one touchdown despite playing all 16 games.
The Packers' only other returning tight end with game experience is Emanuel Byrd, who caught two passes in last year's regular-season finale after he was signed off the practice squad. The team did not select a tight end with any of its 11 draft picks.
The Jaguars released Lewis on March 20 in a move that saved the team $3.5 million on the salary cap.
He told The Associated Press he felt "disrespected" by the Jaguars, who waited until a week after free agency began to make the move.
Lewis is the Jaguars' all-time receptions leader among tight ends with 375 catches for 4,502 yards and 33 touchdowns in 12 seasons with the team.
He is third on the team's all-time receptions and receiving yardage list behind receivers Jimmy Smith and Keenan McCardell.