Cooper attended Miami Northwestern Senior High School in Miami, Florida. As a junior, he missed much of the season with an injury but still managed to be one of Teddy Bridgewater's primary targets and had 16 catches for 175 yards with four scores. Cooper was dominant on the 7-on-7 circuit at various college campuses before his senior season. He had a show out performance at Alabama's summer camp, and that quickly led to an offer from Nick Saban and the Crimson Tide. In his final year, he hauled in 33 receptions for 722 yards and 6 touchdowns. He was a first team FHSAA 8A All-State selection, as well as the No. 4 player on The Orlando Sentinel’s Florida Top 100. He was also invited to play at the 2012 Under Armour All-America Game, where he had a 75-yard touchdown grab and a 93-yard punt return for a score. In addition to being a standout in football, Cooper also starred in basketball and track at Miami Northwestern.
Cooper was a consensus four-star prospect. He was listed as the No. 45 in the Rivals100, and was considered the No. 6 wide receiver and No. 8 player in Florida by Rivals.com. ESPNU listed him as the nation's No. 7 wideout and No. 46 overall prospect in the ESPNU 150 while ranking 25th in the ESPNU Southeast Top 100 and No. 12 in Florida. He was ranked as the No. 6 wide receiver and the No. 10 player in the state of Florida by 247Sports.com, while ranking him 55th in the Top247. Also, Scout.com rated him as the No. 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, Cooper played in all 14 games, including starts in the final nine games. He led Alabama 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 Alabama's 2013 BCS National Championship Game 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.
During Cooper's junior season, he set numerous single-season and career records for Alabama. Against Tennessee, he broke Alabama's single game receiving yards record, finishing with 224. He would later match the record against Auburn. For the season, Cooper had 124 receptions for 1,727 yards and 16 touchdowns, all school records. The 124 receptions were also an SEC record. He became Alabama's all-time leader in receptions (229), 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.
After his junior season, Cooper entered the 2015 NFL Draft.
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 4th pick in the 2015 NFL Draft.
The Oakland Raiders selected Cooper with the 4th 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 his current number, 89. Cooper made his NFL debut for the Oakland Raiders on September 13, 2015. He hauled in 5 receptions for 47 yards in a 33-13 loss to the Cincinnati Bengals. In his second game against the Baltimore Ravens, he connected with Derek Carr for a 68-yard touchdown, the first of his career. Cooper also had 109 yards receiving and helped the Raiders win 37-33. Following up after his week two breakout he provided the Raiders with eight receptions for 134 yards in a 27-20 win against the Cleveland Browns. He is the first Raiders receiver with back to back 100 yards receiving games since Randy Moss in 2005. Through three games he is third in NFL history for receiving yards by a rookie with 290 receiving yards. 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. On December 22, 2015, it was announced Cooper was selected as an alternate for the 2016 Pro Bowl, alongside teammates Derek Carr and Latavius Murray. Cooper replaced Brandon Marshall of the New York Jets on the roster and played in his first Pro Bowl as a rookie.
Cooper put together a solid second season in the NFL. He had 83 receptions for 1,153 yards and five touchdowns. Cooper was named to his second consecutive Pro Bowl on December 20, 2016.