Hester, 33, told ESPN in a text message that he wants to continue playing but declined to discuss his release or any potential landing spots.
Hester missed the first 11 games of the 2015 season as a result of a toe injury, for which he had surgery in January. He did not participate in any offseason activities while recovering.
"He passed his physical," Falcons general manager Thomas Dimitroff said of Hester. "It was a football decision for us in the very end. Again, not to be evasive about it, we wish him all the luck. And we think it's best for the organization for us to move forward."
Falcons coach Dan Quinn said veteran Eric Weems is capable of handling both the kickoff and punt return duties with Hester gone. Justin Hardy, Nick Williams and rookie Devin Fuller are also in the punt return mix, while running back Tevin Coleman, Fuller and Hardy will be involved in the kickoff returns.
Hester, a former second-round draft pick of the Chicago Bears, holds the NFL record for return touchdowns (20), a record he set with the Falcons against the Tampa Bay Buccaneers during the 2014 season. Hester made the Pro Bowl that year with the Falcons.
Hester, a four-time Pro Bowl selection overall, also holds the NFL record for punt return touchdowns (14).
He is the second high-profile player the Falcons have released going into the 2016 season. They also released Roddy White, the franchise's all-time leading receiver, in March.
Hester suffered a turf toe injury after the third preseason game at Miami last season and was placed on injured reserve with a designation to return, but his inability to push off and cut made him functionally ineffective through the final five games of the season. Hester returned nine kickoffs for 235 yards with a long of 35 yards. He returned eight punts for 34 yards with a long of 11.
He wasn't used on offense last season.
Hester was due to make $3 million in 2016 with cap figure of $3,833,334. The Falcons saved $3 million in cap space by releasing him.