Matthews, who played for the Falcons from 2011-14, was released by Tampa Bay on Sept. 3. The Falcons needed more depth on their defensive line after placing defensive end Derrick Shelby on injured reserve with a torn Achilles tendon, ending his season, on Tuesday.
The moves are the latest attempts for the Falcons, who play San Diego on Sunday, to adjust to injuries on defense. They lost veteran linebacker Sean Weatherspoon to an Achilles tendon injury earlier this month and rookie linebackers De'Vondre Campbell and Deion Jones were still limited by ankle injuries in last week's loss at Seattle.
The Falcons on Wednesday also signed linebacker Josh Keyes to their practice squad.
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