Revis, who signed his five-year, $70 million contract Wednesday night, said it wasn't a hard decision to leave the Super Bowl champions. He declined to say whether the Patriots made a competitive offer.
"I'm not going to speak on the numbers," he said on a late-night conference call with reporters. "I think the biggest decision for me was to just come back home. I have a lot of history with the Jets organization, and I just felt like it was, you know, a no-brainer to come home, be back home and make a marriage."
Revis, who played with the Jets from 2007 to 2012, stunned the NFL late Tuesday when he left the Patriots only five weeks after hoisting the Lombardi trophy.
He was lured back to his original team with a blockbuster contract that includes a fully guaranteed $39 million. The Patriots reportedly dropped out when they heard his demands.
Revis hinted that the Patriots missed their chance by declining to exercise the option year in his contract, saying, "You put it in the team's hands if they want to take on the option or not."
The Patriots had until Monday to pick up the option, but it never was a serious consideration because of the amount -- a cap-busting $20 million, the second year of the two-year, $32 million contract he signed last March. They maintained exclusive negotiating rights until 4 p.m. Tuesday, but the two sides never got close to a deal.
Revis spoke positively of his one year in New England, saying it was "really awesome" to learn from "a Hall of Fame coach," Bill Belichick.
"There's no better way to go out than winning a championship," he said.
Only two years ago, Revis was traded by the Jets because of a bitter stalemate in contract negotiations. On Wednesday night, he sounded like he was reuniting with an old flame, saying "there's a lot of love here."
"They drafted me, and I have a lot of history here," said Revis, whose time in New York was tainted by two contract holdouts. "I love being around the people I met in the organization. I just have a lot of ties here. This is where my heart is."
Revis, who lives in South Florida, flew via private jet to New Jersey, landing at 4:40 p.m. in Morristown, a short drive from the Jets' facility. He passed his physical and, after a delay as the two sides pored over language in the contact, he officially became a member of the Jets.
Now, he said, he wants to bring a Super Bowl to the Jets, recalling a vow he made to former general manager Mike Tannenbaum on the day he was drafted in 2007. That won't be easy. The Jets, coming off a 4-12 season, are starting over with a new coaching staff.
"I told [Tannenbaum] I'd do everything in my power to try to bring a championship to this organization, and I still feel that way," he said. "That's something I want to be part of. The thing I want to bring to the organization is winning. That was one of the big reasons to come back home. I still have that mindset."