The move comes four weeks before the beginning of free agency, making Curry an unrestricted free agent.
The eighth-year defensive lineman previously spent time with the Philadelphia Eagles before being released by the team after winning Super Bowl LII in the 2017-18 season. The Bucs signed Curry to a three-year, $23 million deal last March after he refused to take a pay cut with the Eagles.
The Buccaneers saved $8 million on the 2019 salary cap after cutting Curry.
Curry began last season as Tampa Bay's starting left end but was sidelined with an ankle injury. He missed four games, leading to the emergence of Carl Nassib as the team's starter opposite Jason Pierre-Paul.
Curry finished the 2018-19 campaign with 21 tackles, 2.5 sacks, five tackles for loss and seven quarterback hits in 12 games (seven starts).
The Eagles selected Curry in the second round of the 2012 NFL Draft. He spent six seasons in Philadelphia, serving in a backup role in his first five seasons before starting all 16 contests in the Eagles' run to the Super Bowl.
Curry has 152 tackles and 24.5 sacks in 96 career NFL games (23 starts).