The Jets re-signed Morstead to a two-year deal Wednesday, Rich Cimini of ESPN reports.
Morstead signed with the Jets on Friday.
Morstead (illness) is active Week 8 against Detroit
The Dolphins signed Morstead to a one-year contract on Friday, Mike Masala of USA Today reports.
Morstead was waived by the Jets on Monday, Tom Pelissero of NFL Network reports.
Morstead was signed by the Jets on Tuesday.
The Saints released Morstead on Thursday, John DeShazier of the team's official site reports.
Morstead punted three times during Friday's preseason game against the Cardinals and averaged 47.7 yards per attempt.
Morstead (ribs) signed a five-year extension with the Saints on Friday, Joel A. Erickson of the New Orleans Advocate reports.
Morstead played through torn cartilage in his ribs during Sunday's 29-24 divisional-round loss to the Vikings, Josh Katzenstein of The New Orleans Times-Picayune reports.