Janoris Jenkins celebrates following a Rams victory over the Seattle...

Janoris Jenkins celebrates following a Rams victory over the Seattle Seahawks in St. Louis, Mo., Sept. 13, 2015. Credit: AP

The Giants will be taking a major step toward improving their pass defense by agreeing to terms with the top cornerback on the free agency market. And it won’t come cheap.

Janoris Jenkins has agreed to a five-year, $62.5-million deal with the Giants, according to sources. Free agency deals cannot be made official until 4 p.m. Wednesday, and Jenkins is scheduled to arrive in New Jersey on Thursday morning for a physical and to sign the deal that will make him the second highest-paid corner in the NFL behind the Jets’ Darrelle Revis. Jenkins’ deal pays him $40 million over the first three years of the deal and includes $29 million guaranteed. ESPN first reported the agreement and the figures.

That’s what it took to pry him from the Rams, who reportedly offered Jenkins $45 million for five years, an offer he described on Twitter as “total disrespect.” The Raiders also were pursuing Jenkins during the “legal tampering” period of free agency.

It is an uncharacteristic splurge for the Giants, but general manager Jerry Reese has been charged by co-owner John Mara with fixing the team’s roster after three straight losing seasons and four years without making the playoffs. That assignment coincides with the most salary-cap space the Giants have ever had.

And despite the hefty sum for Jenkins, the Giants still have plenty of space under their salary cap. They enter the league year at 4 p.m. Wednesday with just shy of $60 million in room and could flex more from it if they rework Victor Cruz’s cap-heavy contract.

The Giants are far from finished revamping a defense that has struggled the past two years and finished last in pass defense and ranked 30th in sacks. They are one of several teams competing for the services of Olivier Vernon, the defensive end from the Dolphins who had his transition tag dropped on Wednesday making him an unrestricted free agent. Vernon became expendable to the Dolphins when they signed Mario Williams on Tuesday and indicated their desire to keep Cameron Wake as well.

As for the Giants’ pass-rusher in hand, USA Today reported that Jason Pierre-Paul’s one-year deal with the Giants includes $8.5 million guaranteed ($4.25 million base salary, $4.25 million signing bonus) with incentives worth $2 million ($1.2 million in per-game bonuses, up to $500,000 based on his sack total).

Jenkins, 27, was a second-round pick for the Rams out of Florida and North Alabama in 2012 and, despite a red-flagged college career that saw him dismissed from the Gators team after two drug charges, he has missed just four games in the NFL.

Jenkins has been a starter all four years in the league with 10 career interceptions, including five which were returned for touchdowns. He also has surrendered 22 touchdowns during his career.

Jenkins will be paired opposite Dominique Rodgers-Cromartie in the Giants’ secondary. The addition of Jenkins means the Giants are unlikely to retain Prince Amukamara, their former first-round pick who will become a free agent Wednesday afternoon.

Janoris Jenkins

Position: Cornerback

Height/Weight: 5-10/191

Age: 27

Colleges: Florida, North Alabama

Drafted: St. Louis, 2nd round (39th overall), 2002

NFL Stats

Seasons: 4

Games: 60

INTs: 10

TDs: 6 (5 INTs, 1 fumble recovery)

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