The Jets officially announced the deal on Saturday but did not disclose terms. The New York Daily News reported that Cumberland agreed to a three-year deal.
Cumberland was due to become an unrestricted free agent Tuesday, but he would have been allowed to start negotiating with teams at noon Saturday.
The Jets' offseason goal is to add firepower to a unit that finished 31st in passing offense. Despite modest statistics, Cumberland is seen by the organization as an ascending talent.
The Jets are expected to make another significant acquisition at tight end, either through free agency or the draft. They have varying degrees of interest in Jermichael Finley and Brandon Pettigrew, sources said.
The Jets hope to add another offensive piece over the weekend. They're in negotiations with right tackle Austin Howard and hope to re-sign him before he hits the open market.
Before Cumberland's return, the Jets had only two tight ends under contract -- Zach Sudfeld and Chris Pantale, neither of whom has much experience. Veteran Kellen Winslow, set to become an unrestricted free agent, won't be back.
Cumberland, 26, was the Jets' primary tight end last season, although he wasn't a huge factor in the passing game. He caught only 26 balls, but he managed career highs in yardage (398) and touchdowns (four). His impressive yards per catch (15.3) showed his potential as a receiving threat, if used properly. He played for $1.3 million, the tender for a restricted free agent.
The Jets signed Cumberland as an undrafted free agent out of Illinois in 2010. The 6-foot-4, 249-pound Cumberland was a wide receiver in college, but was converted immediately to tight end. He was a non-factor his first two seasons, missing most of 2011 with an Achilles tendon injury. His playing time ballooned the following year as a backup to Dustin Keller.
Cumberland has 58 career catches for 795 yards and seven touchdowns.