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.