Revis, currently recovering from a torn ligament in his left knee, has agreed to a six-year, $96 million contract, NFL.com reported.
Also going to the Jets under the deal will be the Bucs' fourth-round pick in 2014. That could become a third-round pick if Revis is on Tampa Bay's roster on the third day of the 2014 league year.
The deal was made after the Buccaneers were given permission to give Revis a physical.
The 27-year-old, who has feuded with the Jets through two contract holdouts, could have become a free agent after the 2013 season.
He played just two games last year after missing only three contests in his first five seasons.
Revis has logged 19 career interceptions, returning three of them for touchdowns.