The 29-year-old has 52 goals, 42 assists and 141 penalty minutes in 282 regular-season games with Edmonton and the Nashville Predators.
Drafted in the fourth round of the 2004 NHL draft by the Minnesota Wild, Jones' best season came back in 2011-12 with Edmonton when he had 17 goals and 16 assists in 79 games.
The Chatham, Ont., native was slowed by an eye injury suffered during the lockout last season and played in just 27 games, recording two goals and five assists.
Jones posted this message on Twitter shortly after the deal was announced: "Excited to get to wear the Oil drop for another year. Hoping to prove the doubters wrong and help this team return to the 'glory days!'"