Varvaro went 3-3 with a 2.63 ERA in 54 2/3 innings last year, posting a career-high 50 strikeouts in 61 relief appearances. He also posted career highs in walks (2.1) and hits (7.6) per nine innings, while opponents hit .228 against him.
The 30-year-old helps deepen the Red Sox's bullpen, and he will act as a nice complement to relievers Edward Mujica, Junichi Tazawa and Koji Uehara.
This move also helps fill the void of free-agent right-hander Burke Badenhop, who appeared in 70 games for the team last season. The ground-ball guru tossed 70 2/3 innings with a 2.29 ERA.
Over the last two seasons, Varvaro has gone 6-4 with a 2.74 ERA. He is one of just 18 Major League relievers with at least 50 innings logged and an ERA of 2.85 or better.
While Varvaro is a nice addition to the bullpen, the Red Sox are still looking for a left-handed reliever after Andrew Miller signed with the Yankees earlier this offseason.
Kurcz spent this past season with Double-A Portland and went 3-2 with three saves, a 2.14 ERA and 54 strikeouts over 34 games. He allowed just six extra-base hits on the season (all doubles). The 24-year-old also threw for Surprise in the Arizona Fall League this year, going 1-0 with one save, a 3.86 ERA and 15 strikeouts in 10 appearances.
Boston's 40-man roster is now full.
Quinn Roberts is a reporter for MLB.com This story was not subject to the approval of Major League Baseball or its clubs.