The team announced the deal Tuesday, but declined to disclose the terms. NFL.com's Steve Wyche learned Tuesday, from a source with knowledge of the situation, that Jones' deal is for two years.
Jones had career highs of 1,402 yards and 14 touchdowns last season, one year after he was selected for the Pro Bowl following a season in which he ran for 1,312 yards and 13 touchdowns.
Jones, 31, is expected to complement third-year running back Jamaal Charles, who was Kansas City's MVP last season with 1,120 rushing yards and seven touchdowns.
Despite Jones rushing for 1,000 or more yards for the fifth consecutive season, the Jets cut ties with him when free agency began last Friday. Jones was due a $3.3 million roster bonus on top of a $2.8 million base salary this season, and the sides failed to reach a compromise on restructuring the running back's contract. The team wanted Jones to take a pay cut, and he declined.
Jones sat out voluntary activities last offseason while unsuccessfully trying to renegotiate his deal, which was front-loaded over the first two seasons. He made just $900,000 in base salary last season but didn't allow it to affect his play.
Jones was a major reason the Jets ranked first in the NFL with 172.2 rushing yards per game, and he helped the team come within one game of the Super Bowl. He appeared to tire down the stretch as rookie Shonn Greene took the bulk of the carries, but Jones has said he believes he can play another four or five seasons because of the terrific shape in which he keeps himself.
Jones ranks second only to LaDainian Tomlinson, also a free agent, in rushing yards since 2005. Jones ranks 28th on the NFL's career list with 9,217 yards, 190 behind Hall of Famer Earl Campbell.
The Associated Press contributed to this report.