Garrett attended Martin High School in Arlington, Texas, where he was a letterman in football, basketball, and track. In football, he had 19.5 sacks as a senior. Garrett was rated as a five-star recruit by the Rivals.com recruiting network and was ranked as the second best overall player in his class. He committed to play college football at Texas A&M University in October 2013. In track & field, he was a state qualifier in the throwing events, with top-throws of 16.01 meters in the shot put and 50.84 meters in the discus throw.

Garrett came to Texas A&M as the #2 overall prospect in the nation, and the highest-rated defensive player the Aggies had ever signed. As a true freshman in 2014, Garrett broke Texas A&M’s freshman sack record of 5.5 in only six games. In only nine games, he broke Jadeveon Clowney’s SEC freshman sack record of eight. Garrett finished the season with 11.5 sacks (second in the SEC), 53 total tackles, 14 tackles for loss, 10 quarterback hurries, and a blocked kick (which teammate Deshazor Everett returned for a touchdown against Auburn). He was a consensus Freshman All-American and Freshman All-SEC selection. After the conclusion of the season, Garrett announced that he would undergo surgery to repair torn ligaments in his hand, an injury that occurred in the sixth game of the season against Mississippi State.

During the 2015 offseason, Garrett decided to stop using his social media account on Twitter, citing: “There’s a lot of negativity on there I don’t need in my life. I felt like If I want to move forward as a person and as a football player, I don’t need other people’s opinions and other things to stick with me or be in my mind when I have other things to keep doing.” Garrett later resumed using Twitter regularly. Garrett also writes poetry and is working on a dinosaur book for children.

On December 31, 2016, Garrett officially declared his intentions to enter the 2017 NFL Draft.

On December 31, 2016, Garrett announced his decision to forgo his remaining eligibility and enter the 2017 NFL Draft. He was projected to be a top ten selection and was ranked No. 1 on ESPN analyst Mel Kiper Jr.’s big board. Garrett attended the NFL Scouting Combine in Indianapolis and completed the majority of combine drills, but opted to skip the three-cone drill and short shuttle. Garrett solidified his position as a top ten pick with an impressive combine performance. His 41” vertical jump was the top performance of all defensive linemen and he also finished with the second best performance in the bench press and broad jump. Garrett also had the third fastest 40-yard dash of all defensive linemen at the combine, which highly impressed scouts due to his size. On March 30, 2017, Garrett attended Texas A&M’s Pro Day and chose to perform the 40-yard dash (4.65s), 20-yard dash (2.71), 10-yard dash (1.57s), and broad jump (10’6”).

On May 19, 2017, the Cleveland Browns signed Garrett to a fully guaranteed four-year, $30.41 million contract that features a $20.25 million signing bonus, offset language options, and a team option for a fifth year.

On April 30, 2017, two days after the 2017 NFL Draft, Garrett, along with fellow first rounders Jabrill Peppers and David Njoku, were at Progressive Field, and threw out a ceremonial first pitch.

In the 2018 season, Garrett started all 16 games and recorded 13.5 sacks, 44 combined tackles, 12 tackles-for-loss, 29 quarterback hits, three passes defensed, and three forced fumbles. His 13.5 sacks ranked sixth in the NFL that year. He was ranked 49th by his fellow players on the NFL Top 100 Players of 2019.

Garrett was reinstated from his suspension on February 12, 2020. On April 27, 2020, the Browns exercised the fifth-year option on Garrett’s contract. He signed a five-year, $125 million contract extension with the team on July 15, 2020. In Week 2 against the Cincinnati Bengals, Garrett recorded a strip sack on rookie quarterback Joe Burrow which was recovered by the Browns during the 35–30 win. In Week 3 against the Washington Football Team, Garrett sacked Dwayne Haskins twice, including a strip sack that was recovered by himself during the 34–20 win. In a Week 4 game against the Dallas Cowboys, Garrett sacked Dak Prescott twice, one of which was a strip sack that resulted in a turnover, during the 49–38 win. His performance earned him AFC Defensive Player of the Week. In Week 7 against the Cincinnati Bengals, Garrett sacked Joe Burrow two more times and forced a fumble that was recovered by the Browns during the 37–34 win. As the month closed, Garrett won AFC Defensive Player of the Month for October after compiling six sacks, 14 tackles, four for a loss, and two forced fumbles.