"Excited and ready to get to work," Bucannon wrote on social media. "Blessed to have this opportunity!"
Bucannon spent the first five seasons of his NFL career in Arizona, where he played both linebacker and safety. In his second season with the Cardinals in 2015, he recorded a career-best 109 total tackles and three sacks.
The former first-round pick in the 2014 NFL Draft became a free agent after the 2018 campaign and signed with the Buccaneers. He appeared in five games with the Bucs and notched three tackles before he was released in early October.
Bucannon, 27, finished the 2019 season with the New York Giants, playing in nine games and recording 25 tackles.
Bucannon, listed at 6-foot-1, is a versatile defender in the box and could find a similar role in the Falcons' defense, which lost leading tackler De'Vondre Campbell in free agency earlier this off-season.
In 84 career games with the Cardinals, Buccaneers and Giants, Bucannon has tallied 434 total tackles, seven sacks, seven forced fumbles, five fumble recoveries, two interceptions, 12 passes defensed and one defensive touchdown.