The 28-year-old played 44 games with the Jets last season, scoring four goals and adding 12 assists with 18 penalty minutes. His plus-10 rating was the best among all of Winnipeg's defencemen.
The Jets did not release any of the deal's terms.
Clitsome, from Gloucester, Ont., has appeared in 149 NHL games between Winnipeg and the Columbus Blue Jackets with 13 goals and 42 assists. He was drafted by Columbus in the ninth round, 271st overall, in the 2004 NHL Draft.