Moats was born in Norfolk, Virginia, and was raised in Portsmouth, Virginia, where he attended Churchland High School and graduated in 2006. He graduated from James Madison University with a degree in political science. Moats is currently in his second year of earning his master’s degree online, saying he values education greatly. His father is a former marine and current high school math teacher.

Moats was drafted by the Buffalo Bills in the sixth round, 178th overall, in the 2010 NFL Draft. He is the only Buck Buchanan Award winner to be drafted by the Bills. In the Bills 3-4 defensive scheme, he moved from defensive end to inside linebacker, which is an unusual position change considering most defensive ends move to outside linebacker in 3-4 defensive schemes. After several weeks of failing to generate a consistent pass rush, Bills head coach Chan Gailey decided to move Moats to his more natural position of outside linebacker to utilize his pass rushing skill set.

In December 2013, Moats was named the team’s Walter Payton Man of the Year for 2013. Moats earned this honor through his work with the United Way of Buffalo and Erie County and other local groups. Moats was also named the Bills Ed Block Courage Award recipient. He earned this honor by overcoming adversity from an injury and exemplifying courage both on and off the field. He also conducts numerous school visits and takes part in the NFL Play 60 initiative.

On March 24, 2014, the Pittsburgh Steelers signed Moats to a one-year, $795,000 contract with a signing bonus of $65,000. He began his first season with the Pittsburgh Steelers as the backup right outside linebacker behind Jarvis Jones. In the season opener against the Cleveland Browns, he assisted in one tackle during his Steelers debut as they won 30-27. On September 21, 2014, Moats made two solo tackles and sacked Panthers quarterback Cam Newton as the Steelers routed the Carolina Panthers 37-19. The next game, he got his first start with the Steelers in place of an injured Jarvis Jones and made one solo tackle in a 24-27 loss to the Tampa Bay Buccaneers. In Week 9, Moats collected three combined tackles, sacked Ravens quarterback Joe Flacco, and forced a fumble as Pittsburgh defeated the Baltimore Ravens 43-23. The following week, he made a season-high four combined tackles in a 13-20 loss to the New York Jets. He finished the season with 23 combined tackles, four sacks, and two forced fumbles while appearing in all 16 regular season contests and starting ten.

On March 9, 2015, the Pittsburgh Steelers signed Moats to a three-year, $7.50 million contract with a signing bonus of $1.90 million. Moats began 2015 as the left outside linebacker ahead of rookie Bud Dupree. In the second game of the season, he made three combined tackles and was credited with half a sack after taking down San Francisco 49ers quarterback Colin Kaepernick while helping his team rout the 49ers 43-18. On January 3, 2016, Moats racked up a season-high six solo tackles and sacked Cleveland Browns quarterback Austin Davis, helping the Steelers win 28-12. On January 9, 2016, he collected five combined tackles as the Steelers defeated the Cincinnati Bengals 18-16 in an AFC Wild-card matchup. Moats finished the 2015 season with 35 combined tackles, four sacks, and two pass deflections and appeared in all 16 games and started 11.

Moats began the 2016 season as the backup left outside linebacker behind Bud Dupree. He started the season opener in place of an injured Dupree and made one tackle and a pass deflection in a 38-16 win over the Washington Redskins. The next game, Moats collected three combined tackles and sacked Cincinnati Bengals quarterback Andy Dalton, helping the Steelers win 24-16. On November 20, 2016, Moats made two solo tackles and sacked Cleveland Browns quarterback Josh McCown twice, as the Steelers defeated the Browns 24-9.

On July 25, 2018, Moats signed a one-year contract with the Arizona Cardinals. He was placed on injured reserve with a sprained MCL on September 1, 2018. He was released on October 9, 2018.

On June 10, 2019 Moats officially announced his retirement from the NFL via Instagram and Twitter.