Details of the deal weren't revealed.
Dennard reportedly agreed to a three-year, $13.5-million contract with the Jacksonville Jaguars in March, but the two parties failed to finalize terms.
The 28-year-old spent the first six seasons of his career with the Cincinnati Bengals, who selected him in the first round of the 2014 NFL Draft.
Dennard made just nine appearances in 2019 due to injury.
The Falcons parted ways with longtime cornerback Desmond Trufant this offseason. Dennard should provide some veteran leadership to the inexperienced group.