The deal is for one year and $5 million, according to a league source.
With Mark Sanchez out of the picture after being released Friday, Vick and incumbent Geno Smith are expected to compete for the starting job. There was no clarity because no team officials were made available to comment on the quarterback shake-up.
"As of now, Geno is the starting quarterback for this football team," Vick said in a conference call with reporters. "From this point on, we're going to compete every day."
After finishing last season on the Philadelphia Eagles' bench, Vick said recently he wants to be a starter again, so he obviously thinks he will have that shot with the Jets at some point. For now, he wasn't about to make headlines with a bold proclamation. He vowed to support Smith and help him develop.
"I wouldn't say I'd necessarily be OK with sitting on the bench, but I know what I signed up for," said Vick, who described Smith as a good friend. "I know what I came to New York to do. First and foremost, I came to compete and be there for Geno. I know he has a long way to go, but we both talked and we both agree we're going to push one another and make each other better."
Vick, widely regarded as the top free-agent quarterback this offseason, wrapped up the deal -- rumored for weeks -- after a Friday visit with the Jets. He didn't generate a lot of interest on the open market; in fact, the Jets were his first visit. He said a "couple" of other teams were interested, but he declined to name them. A return to the Eagles, he said, wasn't realistic.
Despite an encouraging finish, Smith hasn't received a commitment as the Jets' 2014 starter. General manager John Idzik is philosophically opposed to naming starters. But on Friday, in a radio interview, coach Rex Ryan came close.
"Geno Smith, regardless of who's here at quarterback or who the competition is, is going to be hard to beat out," Ryan said only a few hours before Vick's arrival was announced.
Vick will be reunited with coordinator Marty Mornhinweg, who coached him from 2009 to 2012 in Philadelphia. Vick enjoyed his best all-around season in 2010. His familiarity with Mornhinweg and the coordinator's system played an important role in his decision. They talked about old times Friday at the Jets' facility.
"He's here in a role where he's going to compete and push Geno Smith to become the very best that he can be," Mornhinweg said in a statement.
Vick's play has declined in recent years, partly because of injuries, but he insisted he's not washed up.
"I have a lot left," said Vick, who turns 34 in June. "It was evident with what I was able to do last year. I got injured, and Nick Foles came in and played great. That was the reason I was on the sideline. It wasn't because of my play or because I didn't have anything left in the tank."
Could DeSean Jackson be joining him? The Eagles are said to be shopping their top wide receiver, and the receiver-needy Jets reportedly made an inquiry.
Vick said he doesn't have any inside information, but added: "If there's an opportunity to get DeSean, I'm pretty sure the New York Jets' fans would be in high favor of that. ... If he ends up in New York, I'd be happy, just as happy as he'd be. But who knows? You can't say."
A Jets offseason wouldn't be complete without a significant move at quarterback. They traded for Tim Tebow in 2012 and drafted Smith last year in the second round.
Sanchez was on the verge of claiming the starting job last preseason when he hurt his shoulder. Smith got the job by default, but there was no experienced backup -- a void that might have cost the Jets a playoff spot. Ryan stuck with Smith through a brutal slump, in part because there was no seasoned alternative.
Under pressure after three straight nonplayoff seasons, Ryan wanted Smith insurance. He has that in Vick, who also could serve as a mentor to the young quarterback. Vick said he and Ryan hit it off when they met Friday. Vick said he always wanted to play for Ryan.
Vick won the Eagles' starting job in a preseason competition with Foles last summer. After pulling a hamstring in an Oct. 6 game against the New York Giants, Vick tried to return to the field three weeks later. He aggravated the injury and spent the rest of the season as Foles' backup.
The Eagles signed Vick in 2009, after he served his 21-month federal prison sentence for dogfighting conspiracy and was reinstated by NFL commissioner Roger Goodell. The move was controversial among fans who objected to Vick's dogfighting activities, and because the Eagles already had Donovan McNabb and Kevin Kolb on their roster.
Vick played sparingly in 2009. In 2010, after the Eagles had traded McNabb to Washington, Vick took over the starting job when Kolb was sidelined by a concussion. Vick played some of the best football of his career that season, leading the Eagles to a playoff berth. He was rewarded with a long-term contract but was plagued by injuries (he missed nine of 32 games) and interceptions (he threw 24) in 2011 and '12.
"I want to personally wish Michael Vick and his family all the best as he heads into the next phase of his career in New York," Eagles chairman Jeffrey Lurie said Friday in a statement. "I really enjoyed getting to know him over the last five years. He always represented our team with a tremendous amount of class. Michael was a great teammate, a great leader and we're thankful for everything he provided to our organization and to our community."
Vick said he enjoyed his time in Philadelphia, mentioning his admiration for coach Chip Kelly, but said it "would've been tough" to re-sign with the Eagles.
"[Kelly] wanted better things for me," Vick said. "We all know that Nick deserves to be the starter for that team."
Vick also thanked the Eagles and their fans in a letter he sent to The Philadelphia Inquirer.
"I would like to thank the Eagles and the entire city of Philadelphia. I was honored to be their quarterback and took the privilege to heart every day. I especially want to thank Jeffrey Lurie and Andy Reid, who gave me the opportunity. I want to thank my teammates, who were not just coworkers, but friends. I also want to thank the millions of fans who cheered and supported our team," he wrote.
"The Eagles are an outstanding organization with a bright future, and I'm thankful for all the friendship, love, and support they gave me and my family. I look forward to seeing great things from them both on the field and in the community."
Information from ESPN.com Eagles reporter Phil Sheridan was used in this report.