He appeared in five games with the Peoria Mariners in 2006, his first professional season. He limited opposing hitters to a.184 batting average. Varvaro lost his final two starts of the season on August 22 and August 27, pitching six innings while allowing three runs, two earned. Varvaro spent the 2007 season with the Single-A Wisconsin Timber Rattlers, making 22 appearances, 21 starts. He led Timber Rattlers with 112 strikeouts, while finishing fourth among all Mariners Minor Leaguers in that category. He allowed one run on four hits while striking out nine in a season-high seven innings on June 15 to earn the win. He went 1-1 with a 1.12 ERA, allowing only three runs while striking out 33 in 26 innings from June 10 to July 27. He was placed on the disabled list with a right elbow strain from June 20 to July 8. He struck out at least five batters in 12 games, including striking out a career-high 11 batters in five innings on July 27 against the Great Lakes Loons. Varvaro earned his first career save in only relief appearance of the season, allowing two runs on one hit while walking two and striking out nine in four innings on August 17. He spent the season with the Class-A High Desert Mavericks, appearing in 30 games, 24 starts. He struck out seven or more batters five times, including a season-high nine strikeouts on May 25. He won back-to-back starts May 25 and May 30. He was transferred to the Double-A West Tenn Diamond Jaxx on September 2 for the playoffs and appeared in one game in relief. In 2009 Varvaro split the season with the Mavericks and Diamond Jaxx. He made it to the Southern League All-Star Team. Varvaro participated in the Arizona Fall League playing for the Peoria Javelinas. He was placed on the Mariners' 40-man roster on November 20. On September 22, 2010, Varvaro was called up by the Seattle Mariners along with 4 others following the conclusion of the Tacoma Rainiers season.
Atlanta Braves
On January 13, 2011 the Atlanta Braves claimed Varvaro off waivers. Varvaro was called up from Triple-A Gwinnett in late July 2011 and made a couple of appearances out of the bullpen. He was re-called on September 1, 2011. Varvaro compiled a 2.74 ERA in the 123 appearances he made from 2013–14, as he pitched in varied situations, from long relief to right-handed specialist roles. He was designated for assignment on December 15, 2014.
Boston Red Sox
On December 17, 2014, Varvaro was traded to the Boston Red Sox in exchange for minor leaguer Aaron Kurcz. He was designated for assignment by the Red Sox on April 29, 2015. He then was claimed off waivers by the Chicago Cubs on May 3. However, the Cubs discovered a torn flexor tendon in his pitching arm. As a result, Varvaro was returned to the Red Sox and required season-ending surgery, being subsequently placed on the disabled list on May 24. After recovering, the Sox announced they had signed him to a minor league contract on December 15. In 2016 Varvaro was assigned to Triple APawtucket Red Sox, where he posted a 3-2 record with a 2.83 ERA and one save in 18 relief appearances, striking out 31 batters while walking 13 in 28⅔ innings of work.
