Vellano played for the Maryland Terrapins from 2008–2012. He redshirted his first season in 2008. In the 2009 season, he appeared in four games and recorded one tackle. In the 2010 season, he recorded 63 total tackles, 10.5 tackles-for-loss, five sacks, two passes defended, and one forced fumble. In the 2011 season, he recorded 94 total tackles, 7.5 tackles-for-loss, 2.5 sacks, four passes defended, two forced fumbles, one fumble recovery, and one defensive touchdown. In his final collegiate season in 2012, he recorded 61 total tackles, 14 tackles-for-loss, six sacks, and one interception.
On April 30, 2013, Vellano signed with the New England Patriots as an undrafted free agent. In Week 5 against the Cincinnati Bengals, he received his first career start in place of Vince Wilfork, who was placed on injured reserve. Vellano became a Super Bowl champion on February 1, 2015, helping the Patriots win Super Bowl XLIX over the Seattle Seahawks, 28–24. On August 31, 2015, the Patriots released Vellano. He was re-signed to the practice squad on September 26, and released again on September 30.
Indianapolis Colts
On December 22, 2015, Vellano signed to the practice squad of the Indianapolis Colts.
Second stint with Patriots
On January 26, 2016, the New England Patriots signed Vellano to a futures contract. On September 3, 2016, he was released by the Patriots as part of final roster cuts.
Atlanta Falcons
On September 6, 2016, Vellano was signed to the Falcons' practice squad due to Adrian Clayborn being put onInjured Reserve. He was promoted to the active roster on January 17, 2017. The Falcons ultimately made Super Bowl LI, but lost to Vellano's former team, the New England Patriots. In the game, Vellano had one total tackle. On September 2, 2017, Vellano was waived by the Falcons and signed to the practice squad the next day. He was promoted to the active roster on September 21, 2017. He was waived on October 24, 2017.
Dallas Cowboys
On November 8, 2017, Vellano was signed to the Dallas Cowboys' practice squad. He signed a reserve/future contract with the Cowboys on January 1, 2018. He was waived on March 7, 2018.