Cogliano was drafted by Edmonton 25th overall in the 2005 draft and has not missed a game in four NHL seasons.
Last season, the 24-year-old finished with 11 goals and 35 points.
In 328 games with the Oilers, he has 57 goals and 146 points. He also led Edmonton with a career-high 461 faceoff wins.
The pick acquired for Cogliano gives Edmonton eight selections in the 2013 draft.