Bryant, who will turn 44 in May, had two years and $7 million left on his contract. He was due to make $3.5 million next season. Parting ways with him saves the Falcons $2,833,332 against the 2019 salary cap.
"I am extremely grateful for everything that Matt Bryant has done for this organization over the last 10 years," general manager Thomas Dimitroff said in a statement announcing the move.
"There is no doubt he is one of the all-time great Falcons, as he's been an integral part of our success. This was a difficult decision but one that was necessary for us to move forward into 2019. We have the utmost respect for the person and the player that Matt is, and we wish he and his family the best going forward."
Bryant, the Falcons' all-time leading scorer with 1,122 points, tweeted news of his departure Wednesday morning.
Bryant, who has dealt with some nagging leg and back injuries, went on to say he was looking forward to bringing success and consistency to his next team, with no plans to retire.
During his stint with the Falcons, Bryant made 250 of 282 field goals (88.7 percent), including 36 of 46 from 50-plus yards. He also made 372 of 375 extra points during his 10 seasons with the Falcons. He was named to the Pro Bowl in 2016.
The Falcons likely will turn to Giorgio Tavecchio as their kicker. Tavecchio, who is signed through 2019 and will make $645,000 next season, made all five of his field goals and all eight extra points in place of Bryant last season.
The news comes a day after the Falcons parted ways with starting cornerback Robert Alford, saving $7.9 million against the 2019 salary cap.
Defensive lineman Brooks Reed also indicated on social media that he has been released, thanking the Falcons in an Instagram post for his four seasons with the team. The Falcons would save $4.5 million against the 2019 cap by releasing Reed.