Bowles told ESPN's Josina Anderson in a text message that he was taking the job.
The news came less than four hours after the Jets announced the hiring of Mike Maccagnan as their general manager. Bowles will receive a four-year contract, a source told ESPN NFL Insider Adam Schefter.
The deal is expected to be completed Wednesday morning.
Bowles will join Maccagnan to lead the Jets' new regime as they attempt to rebuild the franchise's credibility after a 4-12 record, its fourth consecutive non-winning season.
The decision to hire Bowles, who spent Tuesday meeting and dining with Maccagnan, owner Woody Johnson and other team officials, comes as a mild surprise because most of the speculation focused on Seattle Seahawks defensive coordinator Dan Quinn.
The Jets might have shifted away from Quinn because rules prohibited them from making an offer until the Seahawks' postseason run is over, which could be Feb. 1 at the Super Bowl.
Johnson & Co. were so smitten with Quinn they were prepared to take a late-night flight to Seattle on Saturday to reel him in if the Seahawks had lost their divisional playoff game. Maccagan, who wasn't hired until Tuesday, would have been on the recruiting trip.
On Monday, the Jets turned their focus to Bowles, inviting him for a second interview. They made sure to schedule it before he returned to the Atlanta Falcons for a second interview, slated for Wednesday.
On Tuesday night, the Jets canceled an interview with Carolina Panthers defensive coordinator Sean McDermott, another indication that Bowles was their new target.
In Bowles, the Jets are getting a highly-respected defensive coach. Despite the loss of several starters, the Cardinals finished fifth in points allowed. Beset by quarterback injuries, the Cardinals rode the defense to an 11-5 record and a Wild-Card berth.
Because of their struggles on offense, the Jets figured to be in the market for a head coach with expertise on that side of the ball, but Johnson hired his fifth straight defensive-minded coach. The Jets haven't had an offensive-minded coach since Rich Kotite in 1996.
The Jets interviewed six other candidates for the position, including three on the offensive side - former Bills coach Doug Marrone, San Diego Chargers offensive coordinator Frank Reich, Seahawks line coach Tom Cable and Jets running backs coach Anthony Lynn.
The only defensive candidates were Bowles, Quinn and McDermott.
Like Maccagnan, Bowles was helped by his connection to Charley Casserly, who, along with Ron Wolf, was hired by Johnson as a consultant during the concurrent searches. Bowles played safety for the Washington Redskins from 1986 to 1990 and 1992 to 1993, when Casserly was the team's general manager. He was a starter on their Super Bowl-winning team in 1987.
After his playing career, Bowles worked briefly under Wolf, the former Green Bay Packers' GM. He was on the Packers' player personnel staff in 1995 and 1996.
This job is a homecoming for Bowles, who grew up in Elizabeth, New Jersey, and spent a season as the Jets' secondary coach (2000). He has coached for six different NFL teams, including three games as the Miami Dolphins' interim head coach at the end of the 2011 season.
From a football standpoint, Bowles is similar to Ryan in that he believes in an attacking 3-4 defensive scheme. Personality-wise, they couldn't be more different. Publicly, Bowles is laid back and guarded, although he has been known to rip into players behind the scenes.