The teams agreed to swap late-round picks in the 2024 draft to facilitate the trade.
Jones, who made the Pro Bowl in 2017, should help bolster Cleveland’s linebacking corps, which has struggled since losing Anthony Walker to a season-ending quad tear in Week 2.
The Browns have surrendered more than 200 yards rushing the past two weeks, including 238 in Sunday’s 30-28 loss to the Los Angeles Chargers.
Jones is the last Falcons player given a lucrative contract under the previous regime to have his situation settled as current GM Terry Fontenot and head coach Arthur Smith look toward the future.
Jones first had his contract restructured earlier this season by converting $8.5 million of base salary to signing bonus, lowering his base salary to $1.14 million and making what had been a hard contract to trade more palatable for teams interested in him.
Jones has been on injured reserve all year after having a shoulder procedure done in the offseason. He was on the physically unable to perform list throughout most of training camp and was activated in the final week, went through two joint practices with Jacksonville and played about a half in the preseason finale against the Jaguars.
Atlanta kept Jones on the 53-man roster but placed him on injured reserve. Jones had been rumored as a possible trade candidate for months, but in August, he said he hadn’t heard much about trade rumors.