The 29-year-old Solder, who won two Super Bowls with the Patriots, was considered the top offensive lineman available in free agency.
Rapoport added Solder agreed to a four-year contract worth $62 million with $35 million guaranteed.
Deals can not be officially signed until Wednesday afternoon at 4 p.m. ET.
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While Solder has never been selected to a Pro Bowl or All-Pro, he has been one of the more solid and consistent left tackles in the league over the course of his career.
The Patriots have expressed interest in defensive end Adrian Clayborn, who might be the best pass rusher in free agency. Butler did not play in Super Bowl 52, a 41-33 Philadelphia Eagles win over the Patriots. A major reason for why the Giants went out and spent a lot on Solder was in due to how poor Erick Flowers has been in the last few years.
The Butler departure isn't a shock with Belichick simply not valuing the player, but the loss of Dion Lewis is interesting with many thinking the running back market wouldn't be much of anything this offseason.
The New Orleans Saints pursued Butler as a restricted free agent past year, but the trade price was too high.
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Last season, Solder allowed six sacks, 10 pressures, 19 quarterback hits and was called for seven penalties.
And while NY definitely has other needs, the draft is right around the corner.
AJ McCarron signed a two-year contract with the Buffalo Bills on Wednesday.
The Giants announced late Wednesday afternoon the signing of former Carolina Panthers cornerback Teddy Williams, who did not play in 2017 after being waived/injured with a shoulder problem.
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