The Stars sent over winger Devin Shore in the deal.
The move adds more veteran experience to the Stars' offensive attack. The 31-year-old Cogliano has 11 points (three goals, eight assists) across 46 games this season. He's missed just two games in his NHL career, spanning 914 contests with the Edmonton Oilers and Ducks.
The 12-year veteran had a two-game suspension between Jan. 15-17, 2018, which ended his long streak of starts. He had the fourth-longest games-played streak in NHL history at 830.
Cogliano has 379 points in his career (159 goals, 220 assists) since being selected in the first round of the 2005 NHL Draft by the Oilers. Edmonton traded Cogliano to the Ducks on July 12, 2011, in exchange for a second-round pick in the 2013 NHL Draft.
"In acquiring Andrew, we are able to add a conscientious player who brings a veteran-presence to our room," Stars general manager Jim Nill said in a statement. "His explosive speed, 200-foot game and iron-man mentality will help our team both on and off the ice."
The 24-year-old Shore has 17 points in 42 games for Dallas this year. Shore failed to record a point in his last eight games, and currently rides a 26-game goal drought.