Adam Schefter of ESPN reported the one-year deal is worth $5 million.
Barrett went undrafted out of Colorado State in 2014 and signed with the Denver Broncos. He spent most of his first season on the practice squad before developing into an impact asset opposite Von Miller.
The 26-year-old Maryland native tallied 151 total tackles, 14 sacks, seven forced fumbles and seven passes defended across 61 games the past four seasons in Denver. He was part of the defense that helped lead the franchise to a Super Bowl 50 title.
Barrett saw his role reduced in 2018 after the arrival of Bradley Chubb, however, and he said in December he wanted a starting role in Denver or elsewhere moving forward.
"I want to start. I want to be a guy somewhere," he told reporters. "I don't want to just be a role player."
Pro Football Focus highlighted the edge-rusher's success before the demotion and his solid performance this past season despite the limited snaps:
He'll look for a return to form in 2019.
Getting a fresh start with the Bucs should provide a major boost to those efforts. He wouldn't have received consistent chances in Denver with the continued presence of Miller and Chubb, so using the free-agent market to find a new home always seemed like the right move.
Barrett should slot in as a starter opposite star outside linebacker Lavonte David in Tampa.