Barrett spent the past five seasons in Denver, starting 15 of 61 regular-season games for the Broncos.
He has 14 career sacks, six forced fumbles and three fumble recoveries during his career. He also appeared in three postseason games with the Broncos.
The Bucs also re-signed defensive tackle Rakeem Nuñez-Roches on Friday.
Meanwhile, the team said it has finalized previously announced agreements with linebacker Deone Bucannon, cornerback De’Vante Harris, wide receiver Breshad Perriman, and punter Bradley Pinion.