The Giants traded Llovera to the Red Sox on Wednesday in exchange for minor-league reliever Marques Johnson.
Llovera was designated for assignment by San Francisco on Saturday and will retain a 40-man roster spot with his new club. The 27-year-old righty holds a 3.92 ERA and 1.09 WHIP through 20.2 frames in Triple-A this season, and he's given up just one run through 5.1 innings in the majors. Llovera doesn't have any options remaining, so he'll likely be used in middle relief out of Boston's bullpen. Kaleb Ort (elbow) was transferred to the 60-day IL to make room on Boston's 40-man roster.