Financial terms and length of contract were not disclosed.
Powell, 26, played in 15 games last season with 141 rushing yards and one touchdown. He also added 11 receptions for 92 yards.
Powell has played each of his four seasons with the Jets, who selected him in the fourth round of the 2011 NFL draft.
He has 1,296 rushing yards, seven touchdowns and 65 receptions in his career.
With Chris Ivory the Jets' likely starter, Powell could contribute as a third-down back. Chris Johnson is a free agent after the Jets declined last month to exercise a team option for 2015.
- Scooby Axson