Stupar immediately joins the Falcons' 53-man roster. The team released veteran linebacker Tim Dobbins, according to Dobbins' agent, David Canter.
The 6-foot-2, 240-pound Stupar was a seventh-round draft pick of the Oakland Raiders in 2012 coming out of Penn State. He spent time on the practice squads in Oakland, Philadelphia and San Francisco before being claimed on waivers by the Jaguars last November.
The 26-year-old Stupar has played in 12 NFL games. His immediately role with the Falcons is expected to be on special teams. He made five special-teams tackles in seven games for the Jaguars last season.
The Falcons assume Stupar's one-year, $495,000 contract.