The 27-year-old Stempniak will be joining his third team in five NHL seasons.
In 61 games with the blue and white, Stempniak has 14 goals and 15 assists with a minus- 10 rating.
Stempniak will be an unrestricted free agent this summer.
Jones (post concussion syndrome) has not played this season due to injury, but has appeared in 106 career NHL games, all with Phoenix, and has collected one goal with 10 assists and 63 PIM. The 26-year-old spent the 2008-09 season with San Antonio Rampage of the American Hockey League.