Yakupov, 18, has played two seasons in the Ontario Hockey League. He has had 80 goals and 170 points in 107 regular-season games.
It is the third straight year Edmonton has had the first choice in the draft. The Oilers have selected forwards Taylor Hall and Ryan Nugent-Hopkins with the other No. 1 picks.
Edmonton won the NHL draft lottery to obtain the top pick. Columbus, the team with the worst record in the NHL last season, chose second and took defenseman Ryan Murray.
The third overall choice went to Montreal and the Canadiens chose a teammate of Yakupov's -- forward Alex Galchenyuk.
The fourth through eighth picks were all defensemen. Griffin Reinhart went fourth to the New York Islanders, followed by Morgan Reilly (to Toronto), Hampus Lindholm (to Anaheim) and Matthew Dumba (to Minnesota).
Carolina dealt the eighth choice to Pittsburgh to obtain Jordan Staal and the Penguins wound up with Derrick Pouliott.
In addition to Staal being dealt from Pittsburgh to Carolina, Dallas made a draft-day trade that sent forward Mike Ribeiro to Washington in exchange for center Cody Eakin and a second-round pick.