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Coming back to the Stars in the deal are prospects Mattias Backman and Mattias Janmark.
The Stars receive a 2015 second-round pick, while the Red Wings get a conditional third-round pick in 2015.
Ansar Khan of MLive reports that the third-round pick the Red Wings received from Dallas goes back to the Stars if Detroit reaches the conference finals.
Backman was a fifth-round selection in the 2011 draft and has yet to appear in the NHL, while Janmark, a 2013 third-round pick, is currently playing for Frolunda HC in Sweden.
Cole, 36, has 18 goals and 15 assists in 57 games.