They believe it so much that they gave JPP a four-year contract worth about $68 million.
"This is where I wanted to be," Pierre-Paul, 28, said on 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 had a strong finish as the Giants made the playoffs.
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."
The Giants rebuilt their defense last year mostly through free agency, adding among others tackle Damon Harrison, who had an All-Pro season, and end Olivier Vernon. Along with Pierre-Paul, they helped turn around the unit and the Giants went 11-5, making the playoffs for the first time since winning the 2011 NFL title.
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 with seven sacks, 53 tackles (35 solo), eight passes defensed, three forced fumbles, and a fumble recovery that he returned for a touchdown.
Former Jets quarterback Geno Smith agreed to terms with the Giants as well, a person with direct knowledge of the move told The Associated Press. The person spoke anonymously because the deal has not been finalized pending Smith passing a physical.