Cooper was a consensus four-star prospect. He was listed as the number 45 in the Rivals100, and was considered the number-six wide receiver and number-eight player in Florida by Rivals.com. ESPNU listed him as the nation’s number-seven wideout and number-46 overall prospect in the ESPNU 150 while ranking 25th in the ESPNU Southeast Top 100 and number 12 in Florida. He was ranked as the number-six wide receiver and the number-10 player in the state of Florida by 247Sports.com, while ranking him 55th in the Top247. Also, Scout.com rated him as the number-12 pass catcher in the nation and 86th overall prospect. He chose Alabama over Florida State, Miami, and Ohio State, among others. Cooper announced his verbal commitment to the University of Alabama on September 22, 2011.

As a freshman at Alabama, Cooper played in all 14 games, including starts in the final nine games. He led the team with 59 receptions for 1,000 yards and 11 touchdowns. The 11 touchdowns broke Alabama’s 62-year-old record by Al Lary. His receptions and receiving yards broke Julio Jones’s Alabama freshman records. In the SEC Championship, he had eight receptions for 128 yards and a touchdown in the 32–28 victory over Georgia. In Alabama’s 2013 BCS National Championship Game 42–14 victory over Notre Dame, Cooper led all Alabama receivers with 105 yards and two touchdowns. Cooper earned consensus Freshman All-American honors and was selected to the SEC All-Freshman team by the league coaches.

As a sophomore in 2013, Cooper played in 12 games with seven starts, missing two games due to injury. He had 45 receptions for a team-high 736 yards and four touchdowns. He had his best game of the season against Auburn in the Iron Bowl, recording six receptions for 178 yards, including a school record 99-yard touchdown reception from quarterback AJ McCarron. In the Sugar Bowl against Oklahoma, he had nine receptions for 121 yards in the 45–31 loss.

As a junior in 2014, Cooper set numerous single-season and career records for Alabama. Against Tennessee, he broke Alabama’s single game receiving yards record, finishing with 224. He later matched the record against Auburn. For the season, Cooper had 124 receptions for 1,727 yards and 16 touchdowns, both school records. In addition, his 124 receptions were an SEC record. He became Alabama’s all-time leader in receptions (228), receiving yards (3,463), and receiving touchdowns (31). Cooper was a finalist for the Heisman Trophy, finishing third behind Marcus Mariota and Melvin Gordon. He won the Biletnikoff Award that season and was also named a unanimous All-American.

Cooper was considered one of the best wide receivers in the 2015 draft class, together with Kevin White. In most mock drafts, he was projected to be a top-10 pick, with some having him as high as the fourth pick in the 2015 NFL Draft.

The Oakland Raiders selected Cooper in the first round with the fourth overall pick in the 2015 NFL Draft. Cooper was initially assigned the jersey number 19, but following the release of fellow receiver James Jones, he switched to number 89. Cooper made his NFL debut for the Oakland Raiders on September 13, 2015. He hauled in five receptions for 47 yards in a 33–13 loss to the Cincinnati Bengals. In his second game against the Baltimore Ravens, he had 109 yards receiving including his first touchdown on a 68-yard pass from Derek Carr. In week 3, he had a franchise rookie record eight receptions for 134 yards in a 27–20 win against the Cleveland Browns, becoming the first Raiders receiver with consecutive 100+ yard receiving games since Randy Moss in 2005. Through three games, his 290 receiving yards were third in NFL history. On November 8, 2015, Cooper passed Tim Brown’s record for rookie receptions (43) in a 35–38 loss to the Pittsburgh Steelers.

On December 20, 2015, Cooper became the first Oakland Raider rookie in franchise history to reach the 1,000-yard mark and the only receiver in the club to reach that same mark since Randy Moss, in 2005. His five 100+ yard receiving games and 72 receptions are also franchise rookie records. On December 22, 2015, Cooper was selected as an alternate for the Pro Bowl, alongside teammates Derek Carr and Latavius Murray; he replaced Brandon Marshall and played.

Cooper put together a solid second season in the NFL. In the season opener against the New Orleans Saints, he had six receptions for 137 yards in a 35–34 victory. In week 5, against the San Diego Chargers, he had six receptions for 138 yards and a touchdown in a 34–31 victory. In week 8, against the Tampa Bay Buccaneers, he had his best game of the season with 12 receptions for 173 yards and a touchdown in a 30–24 overtime victory. Overall, he had 83 receptions for 1,153 yards and five touchdowns. Cooper was named to his second consecutive Pro Bowl on December 20, 2016. He was also ranked 53rd by his peers on the NFL Top 100 Players of 2017.

In the season opener against the Tennessee Titans, Cooper had only five receptions for 62 yards on 13 targets, though one was a touchdown. After having 33 yards in week 2, Cooper had three consecutive games with less than 10 receiving yards. However, on Thursday Night Football, in a 31–30 victory over the Kansas City Chiefs in week 7, Cooper caught 11 passes for a then career-high 210 receiving yards and two touchdowns. His yardage was the most by any NFL player at that point in the 2017 season, the second-most in franchise history, and the first 200+ yard game in franchise history since 1965. With his stellar performance in Week 7, Cooper earned AFC Offensive Player of the Week. After a string of games without stellar yardage totals, Cooper had three receptions for 66 receiving yards and a 63-yard touchdown during a week-16 loss (19–10) to the Philadelphia Eagles. In the season finale against the Los Angeles Chargers, Cooper caught three receptions for 115 yards and an 87-yard touchdown in the 30–10 loss. He was later revealed to have struggled throughout the latter half of the season with an ankle injury that hampered his play. Cooper finished the 2017 season recording career-lows with 48 receptions for 680 yards but did have a career-high seven receiving touchdowns.

On April 22, 2018, the Raiders exercised the fifth-year option on Cooper’s contract. In week 4 against the Cleveland Browns, Cooper caught eight passes for 128 yards and a touchdown in a 45–42 overtime win. During week 6 against the Seattle Seahawks in London, Cooper suffered a concussion and was knocked unconscious. The Raiders went on to lose 27–3.

On October 22, 2018, Cooper was traded to the Dallas Cowboys in exchange for a first-round pick (27th overall, Johnathan Abram) in the 2019 NFL Draft.

In his first game with the Cowboys on November 5, Cooper led the team with five receptions for 58 yards and a touchdown as the Cowboys lost to the Tennessee Titans by a score of 28–14. On Thanksgiving Day, Cooper had eight receptions for 180 yards and two touchdowns, including a 90-yard touchdown catch in the third quarter as the Cowboys defeated the Washington Redskins by a score of 31–23. He was named the NFC Offensive Player of the Week for his performance. During week 14 against the Philadelphia Eagles, Cooper had 10 catches for a career-high 217 yards and three touchdowns. His final touchdown, in overtime, came off a deflection from Rasul Douglas as the Cowboys won 29–23. His 217 receiving yards were the most by one player for a single game in the 2018 season. For his performance, Cooper earned his second NFC Offensive Player of the Week award.

The Cowboys finished atop the NFC East with a 10–6 record and were the number-four seed for the NFC playoffs. In the Wild Card Round victory over the Seattle Seahawks, Cooper had seven receptions for 106 yards. In the Divisional Round loss to the Los Angeles Rams, he had six receptions for 65 yards and a touchdown. On January 21, 2019, Cooper was added to the NFC Pro Bowl roster as an injury replacement for New Orleans Saints wide receiver Michael Thomas. In 15 games on the Raiders and Cowboys rosters during the 2018 season, Cooper accumulated 75 receptions, 1,005 yards, and seven touchdown receptions.

On July 1, 2019, Cooper stated, “I think the change of scenery was really necessary, I really, honestly, don’t think if I would’ve stayed with the Raiders last season that I would’ve been able to flourish and reach some heights that I was able to reach as a Cowboy. So, it was definitely necessary.”

On March 17, 2020, Cooper signed a five-year contract extension with the Cowboys worth $100 million, which featured $60 million guaranteed, $40 million at signing, and a $20 million injury designation that becomes fully guaranteed in 2022.