General manager Mike Tannenbaum said Monday that the team told Jones it will cut ties with him when the league's free agency period begins Friday.
The 31-year-old Jones is coming off a season in which he set career highs with 1,402 rushing yards and 14 touchdowns, helping the Jets reach the AFC championship game.
Jones was due a $3 million roster bonus on top of a $2.8 million base salary this season. He and the Jets failed to reach a compromise on restructuring his contract.
Jones was acquired from Chicago three years ago and has rushed for 3,833 yards and 28 touchdowns.