Giants general manager Dave Gettleman called Pierre-Paul after the trade and told him he received "an offer they couldn't refuse," according to NFL Network.
Pierre-Paul has an $11.25 million salary in 2018. He has a salary cap number of $17.5 million.
The 29-year-old South Florida native had 68 tackles, 8.5 sacks, five passes defensed and two forced fumbles in 16 starts last season for the Giants. Pierre-Paul was the No. 15 overall pick by the Giants in the 2010 NFL Draft. The two-time Pro Bowler and 2011 All-Pro has 58.5 career quarterback takedowns and won a Super Bowl in 2012 with the Giants, helping them knock off the New England Patriots for the second time in five years.
The University of South Florida product is listed at 6-foot-5, 270 pounds.
Pierre-Paul is the latest of several defenders added in the offseason to aid the Buccaneers' pass rush. Tampa Bay also signed defensive end Vinny Curry and defensive tackle Beau Allen from the Philadelphia Eagles in free agency.
Tampa Bay had a league-worst 22 sacks last season, while the Giants ranked 29th in quarterback takedowns.