Cox attended Yazoo City High School in Yazoo City, Mississippi, where he played football and basketball and ran track. Cox played three seasons at Mississippi State University. In football, Cox was named an All-American by Pro Football Weekly as a junior in 2011, after totalling 103 total tackles, including 11 quarterback sacks and two interceptions, one of which he returned for a touchdown. As a senior, he had 104 total tackles, including 10 quarterback sacks, and also added one interception and a fumble recovery. He was selected to play in the Mississippi-Alabama High School All-Star game.
He was also on the Yazoo High track & field team, where he competed in the high jump and in the relays. At the 2009 Division 3-4A Meet, he placed 8th in the high jump event, with a leap of 1.74 meters. In relays, he had personal-best times of 44.32 seconds in the 4 × 100m relay and 1:32.63 minutes in the 4 × 200m relay. He was also credited with a 4.47 time in the 40-yard dash, and benched 300 lb.
Regarded as a four-star recruit by national recruiting web site Rivals.com, he was rated as the No. 5 weak side defensive end in the country, and the No. 2 prospect in the state of Mississippi. He was also considered the No. 17 defensive end prospect in the country by Scout.com. He chose to attend MSU over scholarship offers from LSU, Alabama, Auburn and Ole Miss.
The Philadelphia Eagles traded up from the 15th selection to pick Cox 12th overall in the 2012 NFL Draft. He is the highest selected Mississippi State Bulldog since Michael Haddix in 1983, and the highest selected Bulldog defensive lineman since Jimmy Webb in 1975. Cox was signed to a four-year contract on June 18, 2012.
On October 14, 2012, Cox was ejected after throwing punches against Detroit Lions players, and was fined $21,000. During his rookie year in 2012, Cox played 15 games and finished with 39 tackles, 5.5 sacks, 4 passes defended, and 1 forced fumble.
With the Eagles switching to a 3-4 type defense in 2013, Cox played defensive end. In 2013, Cox started all 16 games and finished with 44 tackles, 3 sacks, 3 passes defended, and 1 fumble recovery. The Eagles finished the season with a 10-6 record to clinch the NFC East, but lost to the New Orleans Saints in the wild card round by a score of 26-24.
The 2014 season was a breakout year for Cox, acquiring 61 tackles, 4.0 sacks, 1 forced fumble, 3 fumble recoveries and 5 run stuffs in 16 games. His presence along the Eagles defensive line led to league-wide recognition and Second-team All-Pro honors.
On April 27, 2015, The Eagles picked up his 5th year option, keeping him with the team through the 2016 season. In a matchup against the Saints in week 5 of the 2015 season, Cox recorded 3.0 sacks and 2 forced fumbles. These matched his season total from 2014 in sacks (4.0) and his career total from 2012-2014 in forced fumbles (2) within only 5 games.
Cox finished the 2015 season with 71 tackles, 9.5 sacks, 2 passes defended, and 3 forced fumbles. For his efforts, Cox received Second-team All-Pro honors and was selected to the Pro Bowl for the first time in his career. He also received the Ed Block Courage Award. He was ranked 49th on the NFL Top 100 Players of 2016.
On June 13, 2016, Cox signed a six-year, $103 million extension with the Eagles with $63 million guaranteed. As a result of a successful 2016 season, Cox was named to his second consecutive Pro Bowl.NFC Defensive Player of the Month for September 2016