Revis signed a six-year extension, which according to multiple media reports is worth $96 million (£63m).
In an unusual move, the deal includes no guaranteed money. Revis missed most of last season after tearing ligaments in his left knee.
In return for Revis the Jets received the Buccaneers' first round pick (13th overall) in Thursday's draft and a conditional fourth-round pick in 2014 that could become a third-round pick.
Taken with 14th overall pick in the 2007 draft by Jets, Revis has started all 79 games in which he has played and has racked up 241 tackles and 19 interceptions returning three touchdowns.
He missed only three games in five seasons prior to his 2012 injury and is one of only two cornerbacks to win an AFC Defensive Player of the Year award in the last 20 years.
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