To make room on the 40-man roster, left-hander Joseph Ortiz was designated for assignment.
Varvaro, 30, has 166 games of major league experience, including nine appearances with the Red Sox this season, when he went 0-1 with a 4.09 ERA. He had been designated for assignment by the Red Sox on April 29.
A former 12th-round draft pick by the Seattle Mariners in the 2005 draft, Varvaro is 7-9 in his major league career with 20 holds and has a 3.23 ERA in stints with the Mariners, Atlanta Braves and Red Sox. In four seasons in the National League with the Braves, Varvaro had a 2.99 ERA over 153 outings, going 6-4 with a 2.74 ERA in his last two seasons in the NL.
Ortiz, 24, was 0-1 with a 3.38 ERA in eight relief appearances at Triple-A Iowa this season.