The 29-year-old Jones 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 draft by Minnesota, Jones' best season came in 2011-12 with Edmonton, where he had 17 goals and 16 assists in 79 games.
The Chatham, Ont., native was slowed by an eye injury during the lockout-shortened 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 Saturday:
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!"
— Ryan Jones (@jonesry28) July 6, 2013
Jets sign defenseman Pardy
The 29-year-old Pardy, who reached a deal with the Jets on Saturday, played in 17 games last season with the Buffalo Sabres. He had four assists and 14 penalty minutes.
Pardy also played in 21 games with Rochester of the American Hockey League and had two goals, seven assists and 22 penalty minutes.
In 200 career NHL games with Buffalo, Calgary and Dallas, Pardy has recorded four goals, 29 assists and 171 penalty minutes.
Selected in the sixth round of the 2004 draft by Calgary, the 6-foot-4, 220-pound Pardy also had a pair of assists in six playoff games with the Flames.
Information from The Associated Press was used in this report.