The length of the deal was announced by the team. Rosenhaus told ESPN that the extension includes $34 million guaranteed for the one-time Pro Bowler.
Jones, a former second-round draft pick from LSU who led the Falcons in tackles during the 2016 and '17 seasons, is considered to be the top coverage linebacker in the NFL.
The deal comes on the heels of the Falcons signing defensive tackle Grady Jarrett to a four-year, $68 million deal that included $38 million guaranteed at signing.
It also leaves wide receiver Julio Jones' contract as the team's most pressing unfinished business prior to the start of training camp. The six-time Pro Bowler, who has two years and more than $21 million remaining on his contract, could be on the verge of becoming the first $20 million-per-year receiver.
Falcons general manager Thomas Dimitroff vowed to address Julio Jones' contract situation after the team adjusted the receiver's contract before last season, netting him an additional $2.9 million for the 2018 season.
As the numbers stand right now, Julio Jones is No. 12 on the NFL's list of highest-paid receivers at $14.25 million per year. From a production standpoint, he boasts five consecutive seasons of at least 1,400 receiving yards and 80 receptions. His career average of 96.7 receiving yards per game tops the all-time list.
Julio Jones said he wouldn't hold out over his contract situation and is due to report to training camp Sunday. There has been optimism about the deal getting done before Monday's first practice, but that's not a guarantee.
The Falcons have continued the trend of rewarding their own draft picks, and briefly made quarterback Matt Ryan the league's highest-paid player with a five-year, $150 million extension ($100 million guaranteed) in May 2018.
With Deion Jones signed, the team now has to start planning for extensions for three other members of the 2016 draft class -- strong safety Keanu Neal, tight end Austin Hooper and linebacker De'Vondre Campbell.
The Falcons already picked up the fifth-year option for Neal, a former first-round pick who is returning from ACL surgery.
There is a chance 2015 first-round draft pick Vic Beasley could earn an extension with a dominant season. The Falcons picked up Beasley's fifth-year option for $12.81 million, but they've made no commitment to the pass-rusher beyond 2019.