The Stars got center Mattias Janmark, defenseman Mattias Backman and a second-round pick this year for Cole and a conditional third-round pick.
The 36-year-old Cole had 18 goals and 17 assists in 57 games for the Stars this season. He has 262 goals and 264 assists in 881 games with Carolina, Edmonton, Montreal and Dallas.
Janmark and Backman, both 22, have not played in the NHL.
Detroit drafted Backman in the fifth round in 2011, and Janmark in the third round in 2013. They have played mostly in their native Sweden, and logged some time with the AHL's Grand Rapids Griffins.