The agreement, first reported by the Boston Globe, is pending a physical and has not yet been confirmed by the club.
Once made official, the deal will represent the largest contract ever given to a pitcher, narrowly edging out Clayton Kershaw's $215m deal with the Dodgers.
Consistently excellent throughout his eight-year major league career, Price has a 3.09 ERA with 1,372 strikeouts and 104 wins.
The left-hander was traded from Detroit to Toronto last season and played a key role as the Blue Jays claimed the AL East crown.
One year earlier, he was traded to Detroit from Tampa Bay, where he spent the early part of his career.
His arrival will be a huge boost for the Red Sox pitching staff, which struggled last season as Boston finished 78-84, last in the division.
That was the second season in a row the Red Sox have finished bottom of the AL East but they are clearly determined to be more successful in 2016, having already acquired premier closer Craig Kimbrel from the Padres this off-season.