The Packers traded Hundley to the Seattle Seahawks on Wednesday for a 2019 draft pick.
Seahawks coach Pete Carroll said the trade has not been finalized, as Hundley has to travel to Seattle and pass a physical.
Hundley went 3-6 in nine starts last season after Rodgers broke his collarbone. Hundley kept the Packers' playoff hopes alive -- but just barely -- for Rodgers' return in Week 15. Green Bay ultimately missed the playoffs for the first time since 2008.
In 2017, Hundley threw for 1,836 yards and nine touchdowns, but he also had 12 interceptions.
The Packers plan to keep both Kizer and rookie Tim Boyle, an undrafted free agent, on their 53-man roster, barring something unforeseen between now and Saturday's final cuts, a source said.
Kizer went 0-15 as the Browns' rookie starter last season and struggled with accuracy (53.6 completion percentage) and turnovers (league-high 22 interceptions). However, Packers first-year general manager Brian Gutekunst, who has repeatedly raved about coach Mike McCarthy and his staff's ability to develop quarterbacks, clearly saw enough improvement in Kizer.
"I definitely see progress and development and improvement," Packers offensive coordinator Joe Philbin said Tuesday.
Hundley, who is in the final year of his rookie contract, now goes from backing up Rodgers to attempting to slide into that role behind Russell Wilson. Incumbent Austin Davis and rookie seventh-round pick Alex McGough have been competing to back up Wilson, and neither has distinguished himself over the summer.
Seattle, like many teams, has typically carried just one backup quarterback, so the job appears to belong to Hundley. If McGough doesn't make the team, he would be a candidate for the practice squad.
Carroll noted that Hundley's experience was among the factors that carried appeal.
"He's played quite a bit and started a bunch of games last year," Carroll said. "... He's big, he runs well, he's got a good arm, he's got good vision of the field, he's made a lot of big throws and big plays.
"He really gives you the thought that he could come in the game and keep it moving. So we thought it was just too good of an opportunity to pass up, and hopefully we'll be able to complete it."
In recent seasons, the Seahawks have either gone with a veteran as Wilson's backup (Tarvaris Jackson and Davis) or a developmental prospect (Trevone Boykin). In Hundley, they now have a backup with both long-term upside and starting experience.
"That's a big part of it," Carroll said of Hundley's experience. "... He's also been in a really good program and coached really well. We think that exposure only helps him.
"... I know he's gained a lot through the time he's been there. Being around Aaron and all that, it could only help you. Mike McCarthy is a great coach, and we have great respect for how they approach the game, so we know he has that in his background as well."
ESPN's Brady Henderson contributed to this report.