Agent Frank Bauer confirmed Sunday that Jones has agreed to a three-year deal with the team.
Financial terms were not disclosed, but Bauer said Jones is glad to be back and the Super Bowl champions are happy to have him.
"Everybody's very, very happy," Bauer said, in a telephone interview with The Associated Press.
Several media outlets reported the deal earlier Sunday, including the Milwaukee Journal Sentinel.
Also Sunday, the Green Bay Post-Gazette reported that the team came to terms with running back John Kuhn.
Speaking to reporters in Green Bay earlier Sunday, Rodgers said he still was holding out hope that Jones and free agent running back John Kuhn both would return to the team.
"I am, yeah, for sure," Rodgers said. "He's an important part of this team. He plays a big role for us. We need to add him back, I think. We need to add John Kuhn back. Those are two guys out there right now who are important to us. It's not my decision, but I'm definitely pulling for those guys to bring 'em back."
Packers coach Mike McCarthy said earlier Sunday that he hoped to have both players back after losing guard Daryn Colledge to the Arizona Cardinals, defensive lineman Cullen Jenkins to the Philadelphia Eagles and backup running back Brandon Jackson to the Cleveland Browns in free agency. The Packers have retained kicker Mason Crosby.
"You're always hopeful to keep your own players," McCarthy told reporters in Green Bay. "So, yeah, I'm hopeful that both of those guys are able to come back. Just like the men that left here. You don't want to lose your own guys, that's for sure. That's the way we're built. We draft them and develop them, but the reality is you can't keep everybody. It's hard to see some go. That's just the nature of our program."
Copyright 2011 by The Associated Press