The deal reportedly would be finalized if Pillar passes his physical this weekend. Boston's position players are not required to report to spring training until Sunday.
Pillar, 31, started last season with the Toronto Blue Jays, then was acquired by the San Francisco Giants in a four-player trade in early April. He combined to bat .259 with a .287 on-base percentage, a .432 slugging percentage, 21 home runs, 37 doubles, three triples and 88 RBIs in 161 games in 2019.
The slugging percentage and homer total were career bests.
Pillar began his career with the Jays in 2013, and he spent parts of seven seasons in Toronto. His career batting line is .261/.296/.405 with 76 home runs and 318 RBIs in 851 games.
The Giants did not offer him a contract after the season, when he was set to become eligible for arbitration, but Pillar is likely to benefit from the move to Boston, which traded Mookie Betts to the Los Angeles Dodgers last week.
Outfielder Alex Verdugo, acquired by the Red Sox in the Betts deal, might not be ready by Opening Day due to ongoing an back/oblique ailment.
Verdugo, then a rookie, sustained the injury in early August, and he missed the rest of the regular season and playoffs. Verdugo batted .294/.342/.475 with 12 home runs and 44 RBIs in 106 games for the Dodgers last season, adding stellar defensive play in the outfield.
--Field Level Media