The deal is for $10.5 million and includes incentives that could boost the total to $12 million, a source told ESPN's Adam Schefter. Bryant also receives a $2 million signing bonus, the source said.
Bryant had been scheduled to become a free agent on March 14, when the new league year officially begins.
Bryant, who will turn 43 in May, told ESPN he has "a few more good years'' left based on his performance over the past two seasons. He made 34 of 39 field goal attempts (87.2 percent) in 2017 and 34 of 37 (91.9 percent) during the Falcons' run to the Super Bowl in 2016.
He led the NFL in scoring with 158 points during the '16 season and has been with the Falcons for nine seasons. Bryant ranks 17th on the NFL's career scoring list with 1,624 points and is 113 points shy of moving all the way up to No. 12.
Bryant missed the final four games of the 2015 season after being placed on injured reserve with a right quadriceps injury. Falcons general manager Thomas Dimitroff praised Bryant for being able to "fight age'' over the past few years.
Bryant originally signed as a free agent with the New York Giants in 2002 and was allocated to NFL Europe. His 16 NFL seasons have also included stints with the Tampa Bay Buccaneers, Miami Dolphins and Indianapolis Colts.
ESPN's Vaughn McClure contributed to this report.