The Chiefs announced the deal Tuesday but declined to disclose the terms.
Jones was released by the Jets last week after being 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; the team wanted him to take a pay cut.
Jones wasn't the only running back on Kansas City's radar. After spending Tuesday with the Washington Redskins, Pittsburgh Steelers free-agent running back Willie Parker was scheduled to visit the Chiefs on Thursday, a league source told Schefter, but the trip was canceled when Jones entered the fold.
The Chiefs also met with Justin Fargas on Tuesday, according to a league source.
Jones sat out voluntary activities last offseason while trying unsuccessfully to renegotiate his deal, which was front-loaded with $13.1 million over the first two seasons. He made only $900,000 in base salary last season, but didn't allow it to affect his play.
The 31-year-old is coming off a season in which he set career highs by rushing for 1,402 yards and 14 touchdowns while helping the Jets reach the AFC Championship Game against Indianapolis. He was also a popular presence in the locker room, twice being voted the team's most inspirational player by his teammates.
Jones had a career-high 331 carries in the regular season and appeared to wear down a bit down the stretch as rookie Shonn Greene got the majority of carries. Still, with the game on the line against San Diego and the Jets facing fourth-and-1 late, coach Rex Ryan put the ball in Jones' hands to make a first down that clinched a trip to Indianapolis.
The 31-year-old is expected to supplement third-year running back Jamaal Charles, who was Kansas City's MVP last season with 1,120 rushing yards and seven touchdowns.
Jones ranks second only to LaDainian Tomlinson, also a free agent, in yards rushing since 2005. Jones ranks 28th on the career list with 9,217 yards, 190 behind Earl Campbell.
Information from The Associated Press was used in this report.