Matthews was signed by the Falcons on Wednesday.
The Falcons had an open roster spot for Matthews after releasing veteran safety Dashon Goldson, who had been plagued by a hamstring issue. Matthews was a member of the team during the 2012, 2013, and 2014 season but recorded a combined 25 total tackles in 32 games.
Matthews was released by the Buccaneers on Thursday, Greg Auman of The Tampa Bay Times reports.
With the 53-man roster deadline approaching, Tampa Bay viewed Matthews as somewhat expendable due to the team's depth at nose tackle. Matthews last played in 2014 when he was a member of the Falcons.