Solder will receive a four-year, $62 million contract with a guarantee of $34.8 million, a source tells ESPN.
The 6-foot-8, 325-pound Solder has spent his entire career with the New England Patriots, who drafted him in the 2011 first round out of Colorado. He is arguably the top free-agent offensive tackle on the market, coming off a season in which he played in every game, protecting quarterback Tom Brady's blind side.
Solder, who turns 30 in April, is the fourth impact player to leave the Patriots. Malcolm Butler and Dion Lewis intend to sign with the Tennessee Titans, according to Schefter, and Danny Amendola is leaving for the Miami Dolphins, as confirmed by ESPN and first reported by the NFL Network.
The Giants also intend to sign outside linebacker Kareem Martin, a source told ESPN, confirming a report by the NFL Network. Martin comes from Arizona and started last year for new Giants defensive coordinator James Bettcher.
Martin, 26, is coming off the best season of his career in the last year of his rookie contract. He had career highs of 23 tackles and 10 starts, and he also had a sack and his first career interception while playing in all 16 games.
Before last season, he hadn't started more than two games.
Solder was an AFC Pro Bowl alternate in 2017. It marked the first time he received a Pro Bowl invitation, although he didn't play in the game because the Patriots were in Super Bowl LII.
Solder has played in 98 career regular-season games, with 95 starts. He has also played in 16 playoff games, starting each of those postseason contests. In 2015, he had signed a two-year. $20.62 million extension with New England.
Solder was the Patriots' 2017 Walter Payton Man of the Year nominee. He previously overcame testicular cancer, and his son, Hudson, was diagnosed with kidney cancer in 2016 and is again undergoing treatments.
"Nate is someone of the highest character. We all respect Nate for what he has done with Hudson and how he is always there for him," coach Bill Belichick previously said.
ESPN's Mike Reiss and Jordan Raanan contributed to this report.