A native of Wilmington, North Carolina, Cooper attended John T. Hoggard High School in Wilmington, where he played football and competed in wrestling and track. He played football as a guard, but also defensive end for the Hoggard Vikings. In his senior year, he paved the way for three players who rushed for 600 yards or more, while Hoggard claimed the state 4-A championship with a 16–0 record. Cooper was voted the conference's player of the year as an offensive lineman. In addition to football, he was also an standout heavyweight wrestler and threw the shot puton the track & field team, recording a top-throw of 14.58 meters at the 2008 NCHSAA 4A East Regional, where he placed 3rd. Regarded as a three-star recruit by Rivals.com, Cooper was listed as the No. 21 offensive guard prospect in his class.
College career
Cooper enrolled in the University of North Carolina at Chapel Hill, and played for the North Carolina Tar Heels football team from 2008 to 2012. After redshirting his initial year at North Carolina, he then started 10 games at left guard and saw action on 579 snaps. He sat out the Connecticut, Georgia Tech and Virginia games due to an ankle injury. Still, Cooper recorded a team-best 40 knock-down blocks on the season and owned a 73-percent grade. He was named to the All-ACC freshman team by The Sporting News. In his sophomore season, Cooper started all 13 games in the regular season and played a team-high 875 snaps. For the second straight year, he led the Tar Heels in knock-down blocks with 55 on the year. Cooper graded out at 83 percent for the season, tied with James Hurst for the best mark on the team. Against William & Mary, he played all 71 snaps and graded out at a season-best 92 percent with seven knock-downs. Cooper earned second-team All-ACC honors at offensive guard. As a junior, Cooper started all 13 games at left guard. He saw action on 864 plays and graded out at 86 percent for the season, good for second on the team. He earned second-team All-ACC honors, and along with left tackle James Hurst, was part of the first Carolina offensive line tandem to earn All-ACC honors since 1993. In 2012, Cooper paved the way for the ACC's leading rusher Giovani Bernard, and was a consensus All-American selection.
Professional career
Cooper was widely considered one of the top guard prospects in the 2013 NFL draft, along with Chance Warmack. After the NFL Combine, Sports Illustrated projected him as the No. 10 overall selection. North Carolina had not seen one of their offensive lineman taken in the first round since tackle Harris Barton was selected in the first round with the 22nd overall pick by the San Francisco 49ers in 1987. Cooper was selected seventh overall by the Arizona Cardinals in the 2013 NFL draft. He was the highest selected offensive guard since Jim Dombrowski in the 1986 NFL draft.
Arizona Cardinals
Cooper was signed to a four-year, $14.55 million contract on July 28, 2013. On August 24, in the third preseason game against the San Diego Chargers, Cooper broke his left fibula. On August 30, the Cardinals placed him on the injured reserve list. It has been speculated that he was never the same player following this injury. In 2014, he was named the starter at left guard even though he was slow to recover from his previous injury and battled through a turf toe and knee injury in training camp. The injuries forced the Cardinals to name Ted Larsen as the starter at left guard to start the season. In week 14 against the Kansas City Chiefs, an ankle injury to left guard Paul Fanaika opened the door for Cooper to have his first career start. He started 2 games until injuring his left wrist against the Seattle Seahawks in week 15. In 2015, he was moved to the right guard starting position after the team signed All-ProMike Iupati, but he suffered a knee injury against the Seattle Seahawks in Week 10 and would lose again his job to Larsen. The Cardinals were planning to move Cooper to center during the 2016 offseason.
On March 15, 2016, Cooper and a second-round draft pick were traded to the New England Patriots in exchange for defensive end Chandler Jones. Cooper was working as a starter at right guard into the third day of training camp, when he suffered a right foot injury that sidelined him, causing him to be passed on the depth chart at guard by Shaq Mason and rookie Ted Karras. He was declared inactive for the first four games until being released on October 8.
Cleveland Browns
On October 10, 2016, Cooper was claimed off waivers by the Cleveland Browns. He was declared inactive in 5 games, until being named the starter at right guard against the Cincinnati Bengals in week 14. He started three of the five games he played. On December 27, Cooper was waived to make room for guard Alvin Bailey, who was being activated from a two-game suspension.
Dallas Cowboys
On January 4, 2017, Cooper was signed by the Dallas Cowboys to provide depth on the offensive line for the playoffs and to evaluate his performance closely, as the Cowboys had been interested in Cooper since the 2013 NFL draft. On March 14, 2017, Cooper signed a one-year contract with the Dallas Cowboys to compete for the vacant left guard job after Ronald Leary departed in free agency, with La'el Collins additionally moving to right tackle. He also was tried at center during Organized Team Activities. He was declared inactive for the first three games. He was named the starter at left guard in the fourth game against the Los Angeles Rams in place of an injured Chaz Green, helping to stabilize the offensive line the rest of the season. He started a career-high 13 games, but suffered a sprained medial collateral ligament in the season finale against the Philadelphia Eagles.
San Francisco 49ers
On March 20, 2018, Cooper signed with the San Francisco 49ers on a one-year deal. He was released on September 1, 2018.
Washington Redskins
Cooper was signed by the Washington Redskins on November 5, 2018, following season ending injuries to starting offensive linemen Brandon Scherff and Shawn Lauvao. He made his first start as a Redskin on November 11, 2018, playing left guard against the Tampa Bay Buccaneers. In a game against the Philadelphia Eagles on December 3, Cooper tore his bicep muscle, ending his season.
Oakland Raiders
On July 15, 2019, Cooper signed with the Oakland Raiders. He was released on September 17, 2019.