Atlanta announced the transaction Tuesday. The Falcons also agreed to a contract with kicker Younghoe Koo. Koo and Elliott Fry worked out for the team Monday.
Bryant made 9 of 14 field goal attempts this season. He missed 2 of 4 field goal attempts during the Falcons' Week 8 loss to the Seattle Seahawks. Bryant, 44, first signed with the Falcons in 2009. He made the Pro Bowl in 2016, while leading the league with 56 made extra points. Bryant led the league by making 93.1 percent of his kicks in 2011.
The Falcons released Bryant in February and re-signed the veteran kicker to a one-year deal in August.
"You always want to make sure that you're consistently evaluating every part of [the team]," Falcons coach Dan Quinn told reporters Monday. "Let's see where we're at, and if there are things we need to look at, we're going to."
Bryant began his career in 2002 with the New York Giants. He also kicked for the Indianapolis Colts, Miami Dolphins and Tampa Bay Buccaneers, before joining the Falcons. Bryant has made 85.6 percent of his career field goal attempts. He ranks No. 11 all-time in career field goals made.
Koo, 25, last appeared during the 2017 season for the Los Angeles Chargers. He made 3 of 6 field goal attempts in four games that season. The Georgia Southern product worked out for several teams before landing with the Falcons. Koo also played for the Atlanta Legends in the Alliance of American Football, before the league disbanded. He made 14 of 14 field goal attempts while with the Legends.
The Falcons will face the New Orleans Saints at 1 p.m. EDT Nov. 10 at the Mercedes-Benz Superdome in New Orleans.