NEW YORK >> The New York Jets have turned to Josh McCown in their winter-long search for a quarterback.

The team announced the signing of the veteran free agent on Monday night, and agent Mike McCartney said on Twitter that the contract is for one season.

Financial terms were not immediately available, but ESPN and NFL Network reported that it is for $6 million fully guaranteed.

McCown met with the Jets over the weekend, but left Sunday without a deal. The sides agreed to a contract a day later.

The Jets had just the inexperienced Bryce Petty and Christian Hackenberg on their roster, and McCown provides a veteran presence who could potentially start and be a mentor to the youngsters.

McCown, who’ll turn 38 on July 4, played the past two seasons with Cleveland. The Jets and general manager Mike Maccagnan had initially showed interest in him in 2015 before New York traded for Ryan Fitzpatrick.

McCown also has familiarity with new Jets quarterbacks coach Jeremy Bates, who was his position coach in Chicago during the 2012 and ‘13 seasons.

New York was in the market for a quarterback with Fitzpatrick a free agent after a poor season and Geno Smith signing with the Giants. The Jets brought in career backup Chase Daniel for a visit Monday, and had been expected to meet with Jay Cutler, who was cut by Chicago two weeks ago, before they signed McCown.

Having McCown in the mix now gives the Jets several options. He has been the ultimate “bridge quarterback” during his career, serving mostly as a backup since being drafted by Arizona in the third round out of Sam Houston State in 2002.

McCown affords New York the ability to continue to evaluate Petty and Hackenberg — and possibly another quarterback if they draft one with the No. 6 overall pick — and knowing it has an experienced player at the position if the youngsters aren’t ready to play.

With the deal for McCown being one year, the Jets also aren’t financially tied to a player who they otherwise might have felt they need to start — which could have been the case had they signed Cutler.

Last season while with the Jets, wide receiver Brandon Marshall raved about McCown’s leadership skills on and off the field while they were teammates in Chicago.

McCown appeared in 13 games over the past two seasons for the Browns, throwing for 3,209 yards, 18 touchdowns and 10 interceptions. But he was 1-10 as a starter with Cleveland, including 0-3 last season, and was released last month.

The well-traveled McCown has also spent time with Detroit, Oakland, Miami, Carolina, San Francisco, Chicago and Tampa Bay. He is 18-42 in 60 NFL starts.

Petty was a fourth-rounder out of Baylor in 2015 and started four games last season, throwing for 809 yards and three touchdowns with seven interceptions before injuring his left, non-throwing shoulder in Week 16.

Hackenberg was a second-round pick last year out of Penn State, but is considered a project and has yet to appear in a regular-season game.