Darnold, 20, was the first quarterback drafted this high by the Jets since Joe Namath went first overall in 1965.
The first round of the NFL Draft is in the books, and may familiar faces from the college football landscape have fulfilled their dreams of making a living playing at the top level.
The Bills are left with just one pick, 96th overall, on Friday after giving up two second-round and a third-round selection after swinging a pair of trades on Day 1.
With the 32nd and final pick of the day a fifth quarterback was selected - the most snapped up in the opening round since 1999 - as the Baltimore Ravens traded up to take 2016 Heisman Trophy victor Lamar Jackson.
New Orleans caused a stir with the biggest trade of Day One at AT&T Stadium in Arlington, moving up from 27th spot to number 14 with Jackson the hottest rumour, but they landed defensive end Marcus Davenport rather than a successor to Drew Brees.
Terrell's selection was announced by Ryan Shazier, the Steelers linebacker who has been battling a serious spinal injury that ended his season in December.
They traded the 65th overall pick in this year's draft to the Buffalo Bills in March to acquire Tyrod Taylor, who is expected to be their starting quarterback this season.
After a Heisman Trophy victor had been the first name off the board in Mayfield, the victor in 2017 was Day One's last name off the board.