Nelson was taken in the fourth round of the 2009 draft by the Bills but played only 17 games for them over the past two seasons. He was suspended four games by the NFL last year for violating the league's substance-abuse policy.
The 6-foot-5 tight end, who worked out with the team last week, end has 20 catches for 181 yards and a touchdown.
The Jets made the announcement Monday, also signing guard Matt Kroul, tackle Dennis Landolt, linebacker Ricky Sapp and tight end Jamarko Simmons to the practice squad. They released linebacker Eddie Jones from the practice squad.