The deal can't be processed until the new league year begins Wednesday.
Beasley, who turns 28 in July, led the NFL with 15.5 sacks in the 2016 season. He had six forced fumbles and four multi-sack games that season, including 3.5 quarterback takedowns against the Denver Broncos.
The Falcons expected the one-time Pro Bowl edge rusher to improve after his breakout second season in the league. Instead, Beasley showed signs of regression, tallying only 18 sacks combined over the last three seasons.
Beasley notched only 1.5 sacks through the first seven games of last season before experiencing a second-half resurgence. He finished with a team-best eight sacks.
Despite Beasley's performance in the second half of the 2019 campaign, the Falcons opted to part ways with him last month.
The Falcons selected Beasley with the No. 8 overall pick in the 2015 NFL Draft out of Clemson. In five seasons in Atlanta, he has recorded 156 total tackles, 37.5 sacks, one interception and 12 passes defensed.