Varnado is known as a defensive specialist and is especially adept at shot blocking aided by his 7'4" wingspan. He led the NCAA in blocks for the 2007–08 season with 157 blocks which tied Shaquille O'Neal for the most blocks in a season in the SEC. In the 2008–09 season, he would break that single season record with 170 blocks. Varnado was named SEC Defensive Player of the Year in 3 consecutive years (2008, 2009 and 2010) becoming the first person to ever do so.
On November 21, 2009, Varnado became the SEC's all-time career block record holder with 413 total blocks in his career. This passed O'Neal's career block record of 412. On January 23, 2010, Varnado surpassed Adonal Foyle on the NCAA's Division I all-time career blocks list to become the second-leading shot-blocker. Needing 8 blocks for the record, Varnado became the NCAA's Division I all-time shot blocker against Alabama on February 24, 2010 passing Wojciech Myrda's record of 535 career blocks.
Varnado is one of just two college players in history to achieve the milestone of 1,000 points, 1,000 rebounds and 500 blocks, the other being David Robinson.
Varnado was drafted by the Miami Heat with the 41st pick in the 2010 NBA draft. However, he signed to play with Carmatic Pistoia, a second-division team in the Italian league, with the Heat maintaining team rights to him. Varnado played 33 games with Pistoia and averaged 15.4 points, 8.9 rebounds, and 3.1 blocks per game.
On September 7, 2012, Varnado was signed by the Heat for summer workout. He was waived on October 26, 2012. After being waived by the Heat, Varnado joined the Sioux Falls Skyforce of the NBA D-League. Varnado was named NBDL player of the week for the first week of the 2012–13 season.
On December 24, 2012, Varnado was signed by the Boston Celtics. On January 6, 2013, he was waived by the Celtics. On January 9, 2013, he accepted a 10-day contract with the Miami Heat, the same team that drafted him in 2010. He was signed to a second 10-day contract on January 20, 2013, and was signed for the rest of the season on January 30. The Heat sent him to the Sioux Falls Skyforce for assignments in March and April 2013. Varnado won his first NBA championship with the Heat when they defeated the San Antonio Spurs 4-3 in the 2013 NBA Finals.
On October 21, 2013, Varnado was waived by the Heat.
On October 31, 2013, he was re-acquired by the Sioux Falls Skyforce. The next day, he was traded to the Iowa Energy. On February 3, 2014, Varnado was named to the Prospects All-Star roster for the 2014 NBA D-League All-Star Game.
On February 18, 2014, Varnado signed a 10-day contract with the Chicago Bulls. On February 28, 2014, the Bulls decided not to sign Varnado to a second 10-day contract.
On March 1, 2014, Varnado signed a 10-day contract with the Philadelphia 76ers. On March 12, 2014, he signed with the 76ers for the rest of the season. On March 29, 2014, he recorded a career high 9 points and 6 blocks in a 123-98 win over the Detroit Pistons.