Agent Drew Rosenhaus told ESPN's Adam Schefter that the deal is worth up to $8.5 million.
Campbell, who turns 27 in July, led the Falcons in tackles last season with 129 to go with 2 sacks, 6 tackles for loss, 2 interceptions and 3 forced fumbles. He developed a chemistry with fellow linebacker Deion Jones and emerged as a vocal leader in the locker room.
The Falcons selected Campbell in the fourth round of the 2016 draft out of Minnesota, and he developed his game in Atlanta under the tutelage of linebackers coach Jeff Ulbrich. Campbell's size (6-foot-4, 232 pounds) and speed made him a versatile performer in coach Dan Quinn's defensive scheme as a player who could also be used as an extra pass-rusher.
Campbell eventually established a reputation for defending top tight ends. He even boldly stated that there was no tight end in the league he couldn't guard successfully.
In four seasons with the Falcons, Campbell had 363 tackles, 5.5 sacks, 5 forced fumbles and 3 interceptions while starting 54 games.
ESPN's Vaughn McClure contributed to this report.