The 28-year-old defenseman had four assists in 37 regular-season games for the Colorado Avalanche, who won the Stanley Cup last season. He did not play in the Stanley Cup Playoffs.
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Murray will join a group of players that includes Philip Broberg, Vincent Desharnais, Markus Niemelainen and Dmitri Samorukov in competing a spot in the Oilers' top six at defenseman. Duncan Keith retired July 12, but Edmonton will return its other top five defensemen from last season: Darnell Nurse, Tyson Barrie, Brett Kulak, Evan Bouchard and Cody Ceci.
Selected by the Columbus Blue Jackets with the No. 2 pick in the 2012 NHL Draft, Murray has 128 points (15 goals, 113 assists) in 432 regular-season games for the Avalanche, New Jersey Devils and Blue Jackets, and three points (one goal, two assists) in 20 playoff games.