David's agents said the agreement extends David's contract for five years and is worth $50.25 million with $25.56 million guaranteed, reports NFL.com's Ian Rapoport.
David would have become a free agent next spring, but he and Bucs general manager Jason Licht had expressed a desire to finalize a contract extension this off-season.
The Buccaneers drafted David in the second round of the 2012 draft. He has started all but two games for the Bucs since then, missing those games in 2014 with a hamstring injury.
David led the Buccaneers with 101 tackles in 2014, and was a first-team All-Pro linebacker in 2013.
Last season, Tampa Bay finished with a 2–14 record, tied for worst in the NFL with the Tennessee Titans.
- Erin Flynn