Hester was released by the Bears earlier this month having spent eight years with the team, during which time he established himself as one of the best return specialists in NFL history.
The 31-year-old has a record 18 career kick and punt returns for touchdowns, while he also equalled Hall of Famer Deion Sanders's record mark of 19 career return touchdowns last season having played 65 games fewer than Sanders.
Hester was used solely as a kick returner last season and averaged 27.6 yards per kick return and 14.2 yards per punt return with one touchdown.
However, the three-time Pro Bowler also previously played as a wide receiver for the Bears, and it is understood that the Falcons will look to use him in that role as well.
Hester had previously expressed his desire to retire with Chicago having been chosen by them in the second round of the 2006 NFL Draft.
However, he now becomes the fifth free agent to join the Falcons from another team, following in the footsteps of defensive tackle Paul Soliai, defensive end Tyson Jackson, guard Jon Asamoah and defensive back Javier Arenas.