The Patriots released Sudfield, 24, on Thursday to add wide receiver Austin Collie.
Sudfeld, at 6-foot-7 and 260 pounds, was signed as an undrafted free agent by the Patriots last May. He was nicknamed "Baby Gronk" after New England tight end Rob Gronkowski.
The Jets released linebacker Scott Solomon to make room for Sudfeld.
The Jets also added 6-5, 215-pound wide receiver David Nelson this week.
"I like that height, especially in the red zone," Jets coach Rex Ryan said. "(It) presents some problems."
The team has had injuries to several wide receivers recently, including Santonio Holmes (hamstring/foot) and Stephen Hill (concussion). Holmes hasn't practiced all week, while Hill was in a red no-contact jersey on Friday. The Jets play Monday night in Atlanta.