Bryant was scheduled to hit free agency when the new league year begins March 14.
"I am ready to play -- I'll play two-three more years in this league," Bryant said in a statement. "There's obviously some curious times ahead to see where those two-three years happen. You know I'd like to finish it here with this organization. I guess I have a history here, so I'd like to finish it up here."
Bryant is set to continue a long career in Atlanta that began in 2009 when he replaced Jason Elam. Since then, the Falcons haven't had to worry about their kicking duties -- Bryant has booted a franchise record 1,029 points, which ranks third among NFL kickers over the last nine seasons. In 2016, he earned his first All-Pro selection after connecting on 34 of 37 field-goal attempts and 56 extra-point attempts. He also hit a 59-yard field goal that season en route to setting a franchise record 158 points that season.
At the age of 42 in 2017, Bryant nailed 34 of 39 FGAs and all 35 PATs. He made eight field goals over 50 yards, including a 57-yarder.
For his career, Bryant has made 85.78 percent of his FGAs, which ranks him ninth all-time among NFL kickers. He's also made 378 career field goals.