Williams attended Mainland High School in Daytona Beach, Florida, where he was a two-sport athlete in football and track. As a senior, he had 103 tackles and 10.5 sacks, helping Mainland to reach the FHSAA 6A state semi-finals, where they lost to Miami Central 7–17. However, the loss was overturned in August 2012 as Miami Central forfeited its entire season due to a transfer infraction.
Considered a four-star recruit by Rivals.com, Williams was ranked as the fifth best strongside defensive end recruit in his class.
As a true freshman in 2012, Williams started nine of 13 games at defensive tackle, recording 64 tackles, eight sacks and an interception. He was named the Pac-12 Defensive Freshman of the Year. As a sophomore in 2013, Williams was moved from tackle to defensive end. After recording 74 tackles and six sacks, Williams was a named a first-team All-Pac-12 selection and was an All-American by ESPN. As a junior in 2014, he recorded 80 tackles and seven sacks. He was named Team MVP, first team All-Pac-12 and was an All-American by the American Football Coaches Association (AFCA) and ESPN.
After his junior season, Williams announced that he would forgo his senior year and enter the 2015 NFL Draft.
In May 2014, Williams was projected a top-4 selection in the 2015 NFL Draft by various mock drafts. By October 2014, Williams was projected as a top-3 selection in the 2015 NFL Draft. In the months leading up to the draft Williams was regularly the 2nd pick in mock drafts, but in the final weeks most experts predicted that Marcus Mariota would instead be the 2nd pick, with Williams subsequently falling to 3-5th place.
Williams was selected by the New York Jets sixth overall in the first round of the 2015 draft. He was the highest selected USC defensive lineman since Darrell Russell in 1997. Williams signed a four-year, $18.6 million contract on May 8, 2015.
Williams made his professional debut on August 11, 2015 in the first preseason game against the Detroit Lions without recording a stat. In Preseason Game 2 against the Atlanta Falcons on August 21, 2015, Williams made 4 tackles, including a sack on T.J. Yates in the endzone for a safety. During Preseason Game 3 against the interleague-rival New York Giants on August 29, 2015, Williams left the game with an apparent knee injury. X-Rays and MRIs were both negative, revealing no ligament damage. On September 7, 2015, he had his jersey number switched to #92 from #62. On his regular season debut against the Cleveland Browns on September 13, 2015, Williams made a total of 5 tackles. On the December 6, 2015, Williams recorded his first full Quarterback sack in a Giants-Jets rivalry game. In 16 games of his rookie year in 2015, Williams made 63 tackles with 3 sacks.
Opening the season against the Cincinnati Bengals on September 11, 2016, Williams had 2.5 sacks for his first career multi-sack game. The Jets combined for 6 sacks, but still lost 22-23. He had a total of 7 sacks on the season, and as recognition for his great play, he was selected as a first-team alternate for the 2017 Pro Bowl.