Terms of the contract weren't immediately available.
The Jets have been linked to other free-agent backs, including C.J. Spiller and Shane Vereen, but their goal was to retain the underutilized Powell.
In truth, they don't have significant interest in Spiller, but they have inquired about Vereen, sources said. The Jets have a solid one-two combination with Chris Ivory and Powell, but they lack a breakaway threat.
Powell, 26, a fourth-round pick in 2011, was the player most affected by Chris Johnson's arrival last season. He became an afterthought as Johnson and Chris Ivory shared the bulk of the ball carrying for the Jets' fourth-ranked rushing offense.
Johnson is gone now, as the Jets declined to pick up his option for 2015. As a result, new general manager Mike Maccagnan made Powell a priority as they approached the free-agency signing period.
Used occasionally as a third-down back, Powell finished with only 33 rushes for 141 yards and one touchdown last season. He also caught 11 passes for 92 yards.
It was a step back for Powell, who was a significant contributor in 2013. Sharing time with Ivory, he ran for a career-high 697 yards, but it wasn't enough to convince the Jets' brass he was worthy of a major role.
Powell's coaches have always liked his game because he's a fundamentally sound player. He's very good in pass protection, and he's one of only nine backs (minimum: 200 carries) who hasn't lost a fumble over the last two seasons.