Coming out of college, Adams was invited to the NFL Combine and performed all the required drills. On May 4, 2017, Adams attended LSU’s pro day and opted to run the 40-yard dash (4.40s), 20-yard dash (2.57s), and 10-yard dash (1.58s) and was able to improve on his combine numbers. He was projected to be a first round pick by the majority of analysts and scouts. Sports Illustrated, DraftScout.com, Pro Football Focus, and ESPN ranked Adams the top safety in the draft.
The New York Jets selected Adams with the sixth overall pick of the 2017 NFL Draft. He was the first defensive back selected in 2017.
On July 20, 2017, the New York Jets signed Adams to a fully guaranteed four-year, $22.25 million contract that includes a $14.32 million signing bonus.
Adams entered training camp competing against Calvin Pryor and fellow rookie Marcus Maye for a role as a starting safety. Head coach Todd Bowles named Adams the starting strong safety to begin the regular season, alongside free safety Marcus Maye.
He made his professional regular season debut and first career start in the New York Jets’ season-opener at the Buffalo Bills and recorded five combined tackles and deflected a pass in their 21–12 loss. Adams made his first career tackle on running back Mike Tolbert after his 13-yard run on the Bills’ first drive. On September 24, 2017, Adams recorded two solo tackles, broke up a pass, and made his first career sack on quarterback Jay Cutler during a 20–6 win against the Miami Dolphins. In Week 17, he collected a season-high ten combined tackles (three solo) and a pass deflection in the Jets’ 26–6 loss at the New England Patriots. He finished his rookie season in 2017 with 83 combined tackles (63 solo), six pass deflections, and two sacks in 16 games and 16 starts.