The Buccaneers announced the deal on Sunday, saying Revis agreed to a new six-year contract.
The deal is worth $96 million, making Revis the highest-paid defensive back in NFL history, but includes no guaranteed money, according to sources close to the Pro Bowl cornerback.
The conditional pick headed to the Jets is a fourth-round selection in 2014, but could become a third-rounder if Revis is on Tampa Bay's roster on the third day of the 2014 league year, sources said.
"We're thrilled. It's rare that you get a chance to add a player of this caliber to your football team. That's what motivated us," Bucs general manager Mark Dominik said.
The Buccaneers formally will introduce Revis during a news conference Monday at noon ET. The front page of the Buccaneers' official team website posted a big picture of Revis in what appears to be a Tampa Bay jersey with the words: "Treasure Island. Darrelle Revis (CB). It's a Bucs Life."
A four-time Pro Bowler during his six-year stint in New York, the 27-year-old Revis addressed Jets fans in a series of tweets Sunday night.
"I been sitting around for the last hour trying to figure out what to say to the Jet Nation & I came up with this," Revis posted on his Twitter account. "The six years I played for the New York Jets were unbelievable. I put my body on the line everyday & did everything could to help the team win.
"I experienced a lot & learned a lot. The memories I had in New York I will keep dearly to my heart. I want to thank all the jets fans for making me feel welcome."
The six-year, $96 million deal would make Revis one of the NFL's two highest-paid defensive players along with Mario Williams.
Jets general manager John Idzik cited multiple reasons for the trade, namely the inability to negotiate a long-term extension with the cornerback and a "degree of uncertainty" regarding Revis' rehab from a serious knee injury suffered last season.
"It became quite evident to us that there is a substantial difference between Darrelle's view of his value and ours," Idzik said Sunday during a conference call. "We felt there would have to be a significant change on either side in order to create a path toward reaching an agreeable deal for either side."
"It was never our intent to proactively go out and shop Darrelle. It was never our goal to have Darrelle leave the Jets. On the contrary, we wanted Darrelle to remain a Jet for the long term, ideally. But Tampa reached out and displayed a sincere and sustained interest in Darrelle."
Revis will not be released before this season, meaning he is assured of making this season's base salary, but his contract includes none of the money that the NFL refers to as "guaranteed." Tampa Bay would be able to release Revis before any season without incurring any salary-cap charge.
The final obstacle to the deal was completed Sunday, when Revis flew on a private plane from New Jersey to Tampa, Fla., to undergo a physical that included a comprehensive checkup on his knee. He passed it, making the trade official.
"We have no concerns about Darrelle Revis' physical condition," a Bucs senior team official told ESPN's Sal Paolantonio. "He will be out there the first day of training camp and ready to go Week 1."
The three sides -- the Jets, the Buccaneers and Revis -- spent the weekend hammering out their respective agreements.
The Jets are now satisfied with the two picks they would receive from the Buccaneers, giving New York the ninth and 13th picks Thursday night.
Revis is happy with the new contract he will receive from the Buccaneers. Plus, with no state income tax in Florida, Revis now will pay less in state tax from the Buccaneers than the $538,200 he would have had he remained with the Jets on his $6 million salary in New Jersey this season.
As if that wasn't enough drama, there's more ahead. In Week 1, the Buccaneers open against the Jets.
Also, in Week 9, in another scheduling quirk, Revis' Bucs play in Seattle at Richard Sherman's Seahawks. The two cornerbacks have traded verbal barbs and tweets this offseason.
Meanwhile, New York is positioning itself well for 2014, when it is expected to receive four compensatory picks to go along with the Buccaneers' pick, meaning the Jets will have a bounty of selections to try to turn around their roster.
And they will do it with added salary-cap space, too. Revis will count $12 million against the Jets' cap this season but nothing in 2014, when New York will be primed with a great chance to upgrade its talent.
Revis is only six months removed from ACL surgery and was cleared to run without restriction only last Monday.
The Bucs, determined to improve their league-worst pass defense, will have added two impact players to their secondary in safety Dashon Goldson and Revis, widely regarded as the best corner in the league.
Jets officials had made it clear that Revis could be had for the right price, a surprising public stance that irked their best player, according to a source.
The latest developments followed years of contract demands and special requests by Revis and his agents.
The most recent dispute occurred when Revis, who had been rehabbing in Arizona, asked to be excused from the first two weeks of the offseason program. The Jets refused.
Revis, with a $1 million workout bonus tied to his participation in the voluntary workouts, showed up to satisfy the clause.
Revis was seeking about $16 million a year in a long-term deal, and Jets owner Woody Johnson told confidantes as far back as January he had no intention of doling out that much for a non-quarterback, sources said.
Johnson denied that, insisting it was "patently untrue" that he had no desire to extend Revis' contract.
Revis was entering the final year of his contract and was due to make $6 million -- $3 million in bonuses and $3 million in base salary. He triggered a $1 million roster bonus March 16, but the Bucs would assume that payment as well as a $1 million workout bonus and $1 million reporting bonus.
The trade speculation started in late January, when Johnson, in private discussions, expressed little confidence in the team's ability to re-sign Revis, according to sources. One league source said Johnson was determined to deal Revis.
"I gathered from Woody that, in his mind, [Revis] was gone," the source said.
Revis said he was "speechless" upon hearing the trade rumors, later indicating he felt insulted that Idzik didn't contact him directly. Idzik reached out, but at no point, publicly or privately, did he say Revis wouldn't be traded.
For two months, the Jets mixed damage control with posturing, claiming their only goal was to make sure Revis returned healthy from his injury. Meanwhile, they continued to shop him.
The Bucs made sense from the outset. They had a glaring need at cornerback, they began free agency with more than $30 million in cap room and their special teams coach, Dave Wannstedt, was Revis' head coach at Pittsburgh.
This would be another splashy addition for the Bucs, who have demonstrated during the last 12 months a willingness to spend big money. They signed wide receiver Vincent Jackson and guard Carl Nicks last year, but finished a disappointing 7-9.
The trade leaves Antonio Cromartie as the Jets' top cornerback, a role he flourished in last season with Revis sidelined by a knee injury. And 2010 first-rounder Kyle Wilson mostly likely would be stepping in as the other starter.
"I believe [Revis] is the best corner in football, without question," Jets coach Rex Ryan said. "But make no mistake, as I mentioned when I took the job five years ago, we will play great defense. The standard we set will not be diminished."
The Revis trade conjured up memories of another blockbuster between the two teams, in 2000, when the Jets traded disgruntled wide receiver Keyshawn Johnson to the Bucs for two first-round draft picks.
Revis' six-year run with the Jets was marked by brilliant play and contract strife.
As a rookie, he missed part of the preseason because of a contract dispute. In 2010, he staged a 36-day holdout that turned ugly, with both sides exchanging jabs in the media. It became a national story as the main plot that summer in the HBO reality show "Hard Knocks," which covered the Jets' training camp.
The two sides settled the dispute with what the Revis camp termed a "Band-Aid" contract. He had three years remaining on his first contract, and that was replaced with a four-year, $46 million deal that included $32 million in guarantees.
At the time, then-GM Mike Tannenbaum called it an "intermediate step" toward a long-term deal that would enable Revis to finish his career with the Jets. Two years into the deal, the Revis camp started dropping hints that he was mulling another holdout.
That never happened, but the two sides continued on a collision course.
Unable to use the franchise tag, per a clause in Revis' contract, the Jets couldn't let him play out his contract because he would've become an unrestricted free agent. So they had to make a decision: Trade him or re-sign him.
ESPN's Sal Paolantonio and The Associated Press contributed to this report.