A source told ESPN NFL Insider Adam Schefter that the deal -- to be signed Tuesday -- is for $7 million, and the 32-year-old will make $3 million guaranteed.
"Paul gives us a veteran presence and I think his experience most certainly will add to what we have already with Kawann and Star. I think he'll be a good compliment to them both," coach Ron Rivera said in a statement Tuesday.
"He's a solid run-defending big man, and at the same time he's a guy that can push the pocket and apply middle pressure on the quarterback. I also think his space-eating ability will allow our linebackers to run."
Soliai was released by the Falcons after he and the team couldn't agree on a paycut that satisfied both sides.
He came over from the Miami Dolphins and signed a five-year, $32 million deal in 2014 that included $14 million guaranteed, $7 million in a signing bonus. He was due to make a base salary of $5 million in 2016 with a cap number of $6,837,500, the third-highest on the team behind quarterback Matt Ryan ($23,750,000) and wide receiver Julio Jones ($15,900,000).
Soliai, a 2011 Pro Bowl selection, was signed to stop the run and take on double-teams to free up the linebackers to make plays in what was more of a 3-4 hybrid defense under former coach Mike Smith. The attacking 4-3 front implemented by coach Dan Quinn decreased Soliai's value and led to less playing time for a player typically not on the field in passing situations.
This past season, Soliai played 348 snaps and finished with 22 tackles, three tackles for loss and five quarterback hits. He showed flashes of his playmaking ability but saw his season cut short by a calf injury that caused him to miss two games and finish the season on injured reserve.
ESPN Panthers reporter David Newton and Falcons reporter Vaughn McClure contributed to this report.