They believe that so much that they have given JPP a four-year contract worth about $68 million.
"This is where I wanted to be," Pierre-Paul told the Giants' website Friday. "I couldn't imagine me being anywhere else."
Two summers ago, on July 4, Pierre-Paul's right hand was severely damaged in a fireworks accident in Florida. He missed the first half of that season, but returned for the final eight games. He started all 12 games he played last year and has a strong finish as the Giants made the playoffs.
The 28-year-old Pierre-Paul said: "I'm back for four years and I'm ready to get after it."
"It means a lot to me, because I started here, and obviously I want to finish here," the two-time Pro Bowler said. "I've seen a lot of guys come and go, especially in my (2010 draft) class. I'm the only one left in my class here. It means a lot. We won a Super Bowl here, and I'm looking forward to putting a fifth trophy in the case."
The team gave Pierre-Paul the franchise tag last month for the second time in three years.
"We're happy to get a long-term deal with Jason," General Manager Jerry Reese said. "Not only is he one of our best players, he is one of our leaders."
Pierre-Paul missed the last four regular-season games and the playoff loss to Green Bay with a core muscle injury that required surgery. He finished the season with seven sacks, 53 tackles (35 solo), eight passes defensed, three forced fumbles, and a fumble recovery that he returned for a touchdown.