Varvaro is 7-9 with a 3.23 ERA, 20 holds and one save in 166 major league appearances with the Seattle Mariners, Atlanta Braves and Red Sox.
Varvaro allowed five runs in 11 innings in nine relief appearances this season with the Red Sox before he was designated for assignment on April 29. The Braves traded Varvaro to the Red Sox on Dec. 17. He was 3-3 with a 2.63 ERA in 61 games with the Braves last season.
Varvaro has held left-handed hitters to a .201 average and right-handed hitters to a .268 average in his career. Ortiz was 0-1 with a save and 3.38 ERA in eight relief appearances with Triple-A Iowa this season.