The 32-year-old Hawk, a veteran of 10 NFL seasons, was released by Cincinnati on April 26, saving the Bengals $1.4 million against the salary cap.
He played just one season for the Bengals, recording 24 tackles and a sack in 15 games in 2015.
Prior to that, the former Ohio State standout spent nine seasons with the Green Bay Packers after being the fifth overall selection in the 2006 NFL draft. He left Green Bay as the Packers' all-time leader with 1,118 tackles and was selected to the Pro Bowl in 2010.
The Falcons were thin at inside linebacker after Weatherspoon ruptured his right Achilles tendon in Sunday's 48-33 victory over the Panthers. The Falcons placed Weatherspoon on injured reserve Tuesday.
In addition, starting weak-side linebacker De'Vondre Campbell has been sidelined since Week 2 with an ankle injury, while backup middle linebacker Paul Worrilow is not expected back for at least another couple of weeks following groin surgery. Starting middle linebacker Deion Jones has a calf injury.
The Falcons' roster stands at 52 after they signed Hawk, released linebacker O'Brien Schofield, waived linebacker Davis Tull off the practice squad and signed punter Michael Palardy to the practice squad. Cornerback Jalen Collins, who was suspended the first four games for violating the league's policy on performance-enhancing substances, is granted a seven-day exemption in which he does not count against the roster. Once he is activated, he will count against the 53-man roster. If the roster remains as is, no corresponding move will have to be made for Collins to be added. But if someone else is signed before Collins is activated, the Falcons will have to release a player to make room for him.
ESPN staff writer Vaughn McClure and The Associated Press contributed to this report.