Braden signed a contract with New England on Monday, Mike Reiss of ESPN.com reports.
Braden spent the past two seasons with AFC East rival New York, suiting up in just three years across that span. The Michigan product will look to add depth across the offensive line if he makes the roster this campaign.
Braden has again been promoted to the Jets' 53-man roster.
This marks the second time this season Braden has been promoted to the team's active roster. He is expected to provide depth on the offensive line. He could end up seeing some work if Kelvin Beachum (back) is unable to suit up.
The Jets signed Braden off their practice squad Wednesday.
Braden's spot on the 53-man roster comes in conjunction with the placement of left guard James Carpenter on injured reserve. The 24-year-old will serve a reserve role on Gang Green's offensive line, and could see snaps on special teams.