Terms of the deal were not disclosed.
Jones-Drew let the Raiders know Thursday night that he wanted to play for Oakland. It's his hometown team and his permanent residence, and there's a decent chance he could start for the Raiders.
With Oakland, Jones-Drew should challenge oft-injured Darren McFadden for the starting job. The fourth overall pick in 2008, McFadden never has played an entire season. He missed three games in 2013.
Jones-Drew, 29, was a first-team All-Pro in 2011 after leading the league with 1,606 rushing yards. He played for Raiders offensive coordinator Greg Olson when Olson was the Jags' assistant head coach/quarterbacks coach in 2012.
Slowed by a foot injury, Jones-Drew averaged just 3.4 yards per carry and rushed for 803 yards and five touchdowns in 15 games last season. He missed 10 games in 2005 because of a foot injury.
Information from ESPN NFL Insider Adam Schefter and ESPN.com Raiders reporter Paul Gutierrez was used in this report.