A person familiar with the negotiations, speaking on condition of anonymity because the deal had not been officially announced, said the 37-year-old Elam would be joining the Falcons.
The NFL Network reported that Elam settled on a four-year, $9 million contract that includes $3.3 million in guaranteed money.
Elam had been the Broncos kicker since 1993, but he's coming home in a sense. He played high school football in suburban Atlanta.
In 1993, Elam kicked a 63-yard field goal against Jacksonville, tying Tom Dempsey's record for the longest field goal in NFL history.
Elam has reached 100 points in each of his 15 seasons and ranks fifth on the career list with 395 field goals and sixth in points with 1,786.
He finished last season with 15 consecutive field goals and kicked four game-winners, the most in the NFL since 1990. He also surpassed John Elway for most games in Broncos history last season.
The Falcons used 47-year-old Morten Andersen the last two seasons, but he doesn't have Elam's range. Andersen, the leading scorer and field goal kicker in NFL history, will have to find another team in his quest to become the league's first 50-year-old player.
Matt Prater would get the first shot at replacing Elam in Denver. He handled kickoff duties in the Broncos' last two games after being waived by Miami and Atlanta last season.
The signing of Elam was yet another major move by the Falcons, who are trying to remake their roster under new general Thomas Dimitroff and first-year coach Mike Smith.
Atlanta, coming off a miserable 4-12 season that fell apart after Michael Vick was linked to dogfighting, already cut tight end Alge Crumpler, running back Warrick Dunn and defensive tackle Rod Coleman in salary-cap moves. On Thursday, they dealt two-time Pro Bowl cornerback DeAngelo Hall to Oakland for a second-round pick this year and a fifth-rounder in 2009.