Jason Pierre-Paul #90 of the New York Giants looks on...

Jason Pierre-Paul #90 of the New York Giants looks on against the New York Jets at MetLife Stadium on Dec. 6, 2015 in East Rutherford, N.J. Credit: Newsday / Mike Stobe

Before they go hunting for other pass-rushers in free agency, the Giants made sure they didn’t lose one that they already had.

Jason Pierre-Paul agreed to a one-year deal with the team a day before he was eligible to become a free agent, a source confirmed. The deal is reportedly worth $10.5 million, although it is unclear how much of that will be in the form of incentives.

“Your boy is back and I am not going anywhere!” Pierre-Paul wrote on Instagram on Tuesday afternoon, after the deal was reached.

While other teams were interested in Pierre-Paul, he ultimately decided to take the Giants’ prove-it deal and remain with the only NFL team he has known, the team that stuck by him through last year’s fireworks accident that nearly cost him his career.

“I would like to thank each and every organization that reached out to my agent during this process especially the Arizona Cardinals,” Pierre-Paul wrote in the Instagram post. “It was hard to decide, but me and my family decided that it’s best for me to stay in New York . . . I have some unfinished business to take care of in New York!!!”

Pierre-Paul had surgery this offseason to improve the use of the remaining fingers on his right hand and potentially allow him to play without a club. If he has a bounce-back season, he could become a 28-year-old free agent at this time next year.

The Giants could also use their franchise tag on him after the 2016 season, or sign him to a long-term deal at any point.

General manager Jerry Reese said last month at the NFL Scouting Combine that while Pierre-Paul’s ability to use his mangled right hand had been diminished, he did not feel as if his other assets were. He also leaned on the relationship between the team and the player as an important piece of the negotiations.

“We know him better, I think, than anybody else would know him,” Reese said. “We’re hopeful that this procedure that he had after the season helps him with respect to the hand injury that he has. I know he’s working hard at it.”

After he was assigned the franchise tag last year, Pierre-Paul played in only nine games following the July 4 accident that cost him his index finger and parts of his thumb and middle finger. He had only one sack, but his impact on the defense was considerable.

“It was obvious when Jason came back last year how disruptive he was without playing football for a long time,” coach Ben McAdoo said at the Combine.

“Just coming in and having a couple weeks to get his feet underneath him, being able to go out and be disruptive as a pass rusher. I just think when you look at him and his ability to get off the ball and get after the quarterback, it’s easy to see and that’s something that comes natural for him.”

The Giants are still expected to be looking to upgrade their pass-rushers. It’s unclear whether they will re-sign Robert Ayers Jr., who led the team with 9.5 sacks in 2015. They have an offer on the table, but he could sign elsewhere in the coming days.

As for outside help, the Giants have expressed interest in Falcons defensive end Adrian Clayborn and while they did not sign Mario Williams, his agreement with the Dolphins could alter the market at the position. Williams’ reported two-year deal in Miami could force the Dolphins to part ways with Cameron Wake and it could also make the Dolphins less likely to match any offers that come to Olivier Vernon, who received the transition tag from the team. That tag allows Vernon to field deals from other teams but gives Miami the right to match any offer.

The Giants are also interested in Jets defensive tackle Damon Harrison, according to a source. Harrison could help solidify the Giants’ run defense; he and Johnathan Hankins would be a formidable duo up the middle.

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