League sources told ESPN and NFL Media that Quinn agreed to a three-year contract with the Cowboys. According to the outlets, the deal matched the length of Cowboys offensive coordinator Kellen Moore's new contract.
Both coordinators will be signed through the 2023 season.
Quinn takes over for former defensive coordinator Mike Nolan, who was fired last week by Cowboys head coach Mike McCarthy. Dallas (6-10) allowed the most points in franchise history (473) and finished 31st in the NFL in run defense this season.
The 50-year-old Quinn was fired as head coach of the Falcons only five games into the 2020 season after joining the team in 2015. He posted a 43-42 record and led the franchise to the Super Bowl in his second season.
Before joining Atlanta, Quinn was the Seattle Seahawks' defensive coordinator in 2013 and 2014. The Seahawks finished No. 1 in yards and points allowed in his two seasons with the team.