The return is the 20th of Hestor's career, and takes him past the previous record he held jointly with Deion Sanders.
"I think it's awesome, and it couldn't happen to a better man," former Bears teammate and retired linebacker Brian Urlacher told ESPN.
"Kind of weird seeing him do it in a Falcons jersey against the coach that drafted him. But an awesome accomplishment for him, though. I'm very proud of him."
Sanders also took to Twitter to congratulate 31-year-old Hester on his achievement.