Cooks was born in Stockton, California to Worth Cooks Sr. and Andrea Cooks on September 25, 1993. Worth Sr. died of a heart attack when Brandin was six years old and Cooks and his three brothers, Fred, Worth Jr., and Andre, were thereafter raised by their mother. He attended Lincoln High School in Stockton, where he played high school football for the Trojans. As a sophomore, he recorded 29 receptions for 600 yards and seven touchdowns. As a junior, he had 46 receptions for 783 yards and 10 touchdowns, while also collecting three interceptions on the defensive side of the ball. As a senior, he had 66 receptions for 1,125 yards and 11 touchdowns. Cooks was ranked by the Rivals.com recruiting network as the 26th-best wide receiver and the 240th overall prospect in his class. He originally committed to play college football at the UCLA but changed to Oregon State University. In addition to football, Cooks played basketball and ran track in high school.

In his first NFL game, Cooks caught seven passes for 77 receiving yards and a receiving touchdown and had one rush for 18 yards in a 37–34 overtime road loss to the Atlanta Falcons. This made Cooks the youngest player, at 20 years and 347 days, to catch a touchdown pass since Reidel Anthony caught one against the Miami Dolphins on September 28, 1997, at 20 years and 343 days. In Week 3, against the Minnesota Vikings, he had eight receptions for 74 receiving yards in the 20–9 victory. In Week 5, against the Tampa Bay Buccaneers, he had a season-high nine receptions for 56 receiving yards in the 37–31 victory. During Week 8 against the Green Bay Packers, Cooks recorded six catches for 94 receiving yards and a receiving touchdown to go along with a four-yard rushing touchdown in the 44–23 road victory. Two weeks later against the San Francisco 49ers, he caught five passes for 90 receiving yards and a receiving touchdown in the 27–24 loss. In the next game against the Cincinnati Bengals, Cooks had five receptions for 50 receiving yards and a five-yard rush before leaving the eventual 27–10 defeat with an injury. It was later revealed that he broke his thumb, prematurely ending his rookie season.

Overall, he had 128 receptions, 1,730 receiving yards, and 16 receiving touchdowns. Cooks’s receptions and receiving yards were Pac-12 records. He was held to under 100 yards only four times and exceeded 200 yards in a game twice. At the end of the season, he won the Fred Biletnikoff Award and was a consensus All-American. He was the second Oregon State player to win the Biletnikoff Award, the first being Mike Hass in 2005. He finished his collegiate career among the best in school history by being second in receptions, third in receiving yards, and first in receiving touchdowns.

Cooks started his sophomore season with six receptions for 80 receiving yards and one receiving touchdown in a 10–7 victory over Wisconsin. Two weeks later, against UCLA, he had six receptions for 175 receiving yards and one receiving touchdown in the 27–20 victory. In the following game against Arizona, he had nine receptions for 149 receiving yards in the 38–35 victory. On October 13, against BYU, he had eight receptions for 173 receiving yards in the 42–24 victory. On October 27, against Washington, he had nine receptions for 123 receiving yards and one receiving touchdown in the 20–17 loss. On November 3, against Arizona State, he had six receptions for 116 receiving yards in the 36–26 victory. Overall, he had 67 receptions for 1,151 yards and five touchdowns. The combination of Cooks and Markus Wheaton created one of the most dynamic receiving duos in college football and Oregon State history. The two players combined for 158 receptions, 2,395 yards, and 16 touchdowns in the 2012 season.

On January 2, 2014, Cooks announced that he would forgo his senior season and enter the 2014 NFL Draft.

On May 18, 2014, the Saints signed Cooks to a four-year contract worth $8.3 million.

Cooks finished the 2019 season with 42 receptions for 583 receiving yards and two receiving touchdowns, all his lowest totals since his rookie season in 2014.

Cooks finished the 2016 season catching 78 receptions for a then career-high in receiving yards with 1,173 and eight touchdowns. Despite the fact that his targets dropped from 129 in 2015 to 117 in 2016, his 10.0 yards per target ranked sixth among NFL wide receivers.

Before the 2016 season, Cooks was pegged as a breakout candidate by ESPN. He lived up to the pre-season hype when he had six receptions for 143 receiving yards and two receiving touchdowns and an 11-yard rush during the season-opening 35–34 loss against the Oakland Raiders. He caught a 98-yard touchdown pass in the third quarter to set the Saints’ franchise record for the longest play. Cooks, along with Willie Snead IV and rookie Michael Thomas, finished the day with 373 receiving yards combined, the most ever by a New Orleans trio in a loss. During Week 6 against the Carolina Panthers, Cooks had seven passes for 173 receiving yards, which included a 87-yard touchdown reception, in the 41–38 victory. In the next game against the Kansas City Chiefs, he recorded seven receptions for 58 receiving yards and a receiving touchdown in the 27–21 loss. The following week, Cooks recorded four receptions for 44 receiving yards and a receiving touchdown in a 25–20 victory over the Seattle Seahawks. Two weeks later, he caught three passes for 98 receiving yards and a receiving touchdown in a 25–23 loss to the Denver Broncos. After a Week 12 49–21 win over the Los Angeles Rams, in which he was not targeted for a single pass, Cooks voiced his frustration by saying, “Closed mouths don’t get fed.” During a Week 15 48–41 road victory against the Arizona Cardinals, he caught seven passes for a career-high 186 receiving yards and two receiving touchdowns, one for 65 yards and one for 45 yards. In the next game against the Tampa Bay Buccaneers, Cooks recorded five receptions for 98 receiving yards in the 31–24 victory. In what would be his final game with the Saints, he had three receptions for 19 receiving yards in the 38–32 loss to the Atlanta Falcons in Week 17. The Saints finished with a 7–9 record and missed the playoffs.

Cooks is a Christian. He followed big plays in the 2016 season with a bow-and-arrow motion, referencing a Bible verse in which a boy named Ishmael used his archery skills to survive in the desert after he nearly died there without water.

On March 10, 2017, the New England Patriots traded their 2017 first-round (used on Ryan Ramczyk) and third-round draft picks (one was originally acquired from the Cleveland Browns in exchange for Jamie Collins) to the Saints for Cooks and a 2017 fourth-round draft pick. On April 29, 2017, the Patriots picked up the fifth-year option on Cooks’ contract.

On September 7, 2017, Cooks made his Patriots debut against the Kansas City Chiefs in the NFL Kickoff Game. He had three receptions for 88 receiving yards in the 42–27 loss. During a Week 3 36–33 victory over the Houston Texans, Cooks had five receptions for 131 receiving yards and scored his first two touchdowns as a Patriot, including a 25-yard game winner with 23 seconds left; after the game-winning touchdown, he scored on the ensuing two-point conversion. Two weeks later against the Tampa Bay Buccaneers, Cooks caught five passes for 85 receiving yards in the 19–14 road victory. In the next game, he had six receptions for 93 receiving yards in a 24–17 victory over the New York Jets. The following week, Cooks recorded four receptions for 65 receiving yards and a receiving touchdown in a 23–7 victory over the Atlanta Falcons. After a Week 9 bye, the Patriots went on the road to face the Denver Broncos. In that game, Cooks caught six passes for 74 receiving yards as the Patriots won by a score of 41–16. In the next game against the Oakland Raiders at Estadio Azteca, he had six receptions for 149 yards and a season long 64-yard touchdown in a 33–8 victory. The following week against the Miami Dolphins, Cooks caught six passes for 83 receiving yards and a receiving touchdown and had an 11-yard rush in the 35–17 victory. Through Week 12 of the 2017 season, he led all players in receptions of 40+ yards, with six. Three weeks later against the Pittsburgh Steelers, Cooks recorded four receptions for 60 receiving yards and a receiving touchdown in the 27–24 road victory. In the regular-season finale against the Jets, he caught five passes for 79 receiving yards and a receiving touchdown and rushed thrice for eight yards as the Patriots won by a score of 26–6.

On April 3, 2018, the New England Patriots traded Cooks and a fourth-round draft pick to the Los Angeles Rams for a first-round pick (used on Isaiah Wynn) and a sixth-round pick. On July 17, 2018, Cooks signed a five-year, $81 million extension with the Rams with $50.5 million guaranteed.

On April 10, 2020, Cooks and a 2022 fourth-round draft pick were traded to the Houston Texans in exchange for the Texans second-round draft pick in the 2020 NFL Draft.

In 2020, Cooks donated $50,000 to his hometown of Stockton, California. The donation helped establish the Stockton’s Children’s Fund, which serves local children impacted by the coronavirus pandemic.