Solder will become the highest-paid offensive lineman in the league with a four-year contract worth $62 million, including $35 million guaranteed, according to the NFL Network's Ian Rapoport.
Deals cannot be officially signed until Wednesday afternoon at 4 p.m. ET.
The 6-foot-8, 314-pound Solder has been a mainstay on the Patriots' offensive line, starting at least 15 games in six of his seven NFL seasons.
Solder, 29, who protected the blind side of four-time Super Bowl MVP Tom Brady, had signed a two-year, $20.6 million contract with the Patriots in 2015.
During his tenure in New England, Solder appeared in four Super Bowls, including a loss to the Giants during his first season in 2011, when he was named to the NFL's All-Rookie team.
A first-round draft pick out of Colorado in 2011, Solder started 95 of 98 regular-season games and 16 postseason contests for the Patriots.