Ian Rapoport of NFL Network reported the 23-year-old Texas native will earn a 53-man roster salary despite his placement on the practice squad.
Webb didn't play in any regular-season games for the Giants last season. The team opted to start veteran Geno Smith rather than the rookie when it benched Eli Manning in November.
The 87th overall pick in last year's draft completed 61.5 percent of his throws with 83 touchdowns and 34 interceptions across four collegiate seasons with the Texas Tech Red Raiders and Cal Golden Bears.
He failed to reach expectations with New York, though.
Webb connected on just 52.9 percent of his 34 throws with no touchdowns in the 2017 preseason and posted a 52.8 percent completion rate with one score on 53 attempts during this year's exhibition slate.
After he failed to deliver standout performances during training camp over the past two seasons, the Giants decided to move forward with Kyle Lauletta and Alex Tanney behind Manning.
"I think there are a couple things [to work on]," Webb told reporters before Big Blue's final preseason contest. "Be more consistent passing the football, finding completions and continue to get better. I think I have taken a lot of steps each and every week."
Now, he'll look to take advantage of a fresh start with the Jets. It's unlikely he'll see playing time during the 2018 campaign, but he'd probably be elevated to the active roster if either rookie starter Sam Darnold or veteran backup Josh McCown suffers an injury.