Terms were not disclosed, but a source told ESPN's Adam Schefter on Friday that it is a five-year deal.
Pugh, 27, was the Giants' top lineman when on the field the past few seasons, playing well despite a relative lack of talent elsewhere on the line. He also impressed while bouncing back and forth between right tackle and left guard.
The 2013 first-round pick out of Syracuse started his career at right tackle, before shifting to right guard and landing back at right tackle this past season when the Giants were desperate on the outside. His versatility is a plus.
But Pugh does come with risks. He has an injury history after missing 17 games over the past four seasons, including the final eight of last season with a back injury.
Pugh did not need surgery and has been training without restrictions this offseason.
The Giants picked up the fifth-year option on Pugh for the 2017 season, but they never really had serious negotiations about a long-term deal during the final years of his rookie contract. Pugh earned $8.8 million in 2017 but had been eyeing the significant payday that comes with free agency for several seasons -- and it didn't hurt that this year's free-agent class was especially weak at the position.
"If I could build you the perfect equation and kind of factor in how much those mean to me -- it all goes into it," Pugh said after the season. "I want to win. I want to win now. I've been here five years. I only made the playoffs one time."
ESPN's Jordan Raanan contributed to this report.