The person, who requested anonymity because the deal has not been announced, said the Jaguars will receive a conditional seventh-round draft pick in exchange for Smith. The deal was reported by ESPN earlier Sunday night.
It will be Smith's second stint in Green Bay. The Packers signed him as a free agent in 2009 but cut him before the start of the season, a move that was publicly criticized at the time by veteran cornerback Charles Woodson.
It was a much-needed move this time around for the Packers (3-3), who came into the season with Super Bowl expectations but have been hit hard by injuries at several positions and now have lost two straight games in overtime.
Green Bay lost at Washington last week and was beaten at home by Miami on a field goal Sunday.
Veteran safety Atari Bigby began the season on the reserve/physically unable to perform list for the Packers after having ankle surgery at the beginning of training camp.
He was replaced by rookie Morgan Burnett, a third-round draft pick out of Georgia Tech, but Burnett tore his anterior cruciate ligament in a victory over Detroit earlier this month. Backup Derrick Martin also is on injured reserve with a knee injury.
Bigby is eligible to come off the PUP list this week, as is cornerback Al Harris, who is recovering from last year's season-ending knee injury. But the trade for Smith could be an indication that Bigby might not be ready to play right away.
Smith started three games for Jacksonville at strong safety this season -- all wins. He missed two games with turf toe.
His best game came against Indianapolis two weeks ago, when he made two potential touchdown-saving plays. He forced a fumble at the 10-yard line and picked off a pass at the 4.
The Jaguars have overhauled their secondary since training camp. They traded Reggie Nelson to Cincinnati, re-signed Gerald Alexander after releasing him and now parted ways with Smith.
Smith became expendable when the team started grooming former cornerback Don Carey to play safety. Carey played well in limited action there last week at Buffalo.
The Jaguars could have Carey and strong safety Courtney Greene -- both second-year players -- in the starting lineup Monday night against Tennessee.