The Browns traded their 2024 sixth-round draft pick to the Falcons in exchange for Jones and the Falcons' 2024 seventh-round selection.
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.
"If I would have known something, if it was something serious, Art would have called me," Jones said. "My agent would have called me."
The Falcons had already, in many ways, moved on from Jones. They signed Rashaan Evans to a one-year deal this offseason, had plans for Mykal Walker to take over at the other inside linebacker position and drafted Troy Andersen in the second round of this year's draft as a potential future starter.
Evans and Walker have been Atlanta's starters this year and Andersen an improving backup, making the possibility of Jones returning to the Falcons even more unlikely.
Jones started 83 of 85 games he played in Atlanta with 652 tackles, 11 interceptions -- five returned for touchdowns -- 44 passes defended and 8.5 sacks.
ESPN's Michael Rothstein contributed to this report.