The Oilers landed the top pick despite having only the second-worst record in the league this season -- the Columbus Blue Jackets finished 30th overall.
Edmonton had an 18.8-percent chance to win the lottery.
The Oilers used their first-overall picks in the last two years to draft forwards Ryan Nugent-Hopkins (2011) and Taylor Hall (2010).
Columbus -- which had a 25 percent chance -- will go second when the draft is held June 22-23 in Pittsburgh.
The Blue Jackets will be followed by the Montreal Canadiens, the New York Islanders and Toronto Maple Leafs.
The top prospect is considered to by Ontario Hockey League forward Nail Yakupov.
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