Yakupov, a dazzling skater rated the best offensive player available, had 31 goals and 69 points in 42 games last season for the Ontario Hockey League's Sarnia Sting.
His addition gives the Oilers a trio of young, dynamic forwards, after they used the first overall selection in 2011 on Ryan Nugent-Hopkins and the top pick in 2010 on Taylor Hall.
"The natural ability, the skill set that Nail has is elite and we've been talking about elite athletes coming to our organisation," Oilers general manager Steve Tambellini told reporters at Pittsburgh's Consol Energy Center.
"He's dangerous, he's hungry to score goals and I think he's a pretty good fit with the people we already have."
The Columbus Blue Jackets, who earlier in the day sent three later round picks to the Philadelphia Flyers for netminder Sergei Bobrovsky, held onto the second overall selection and used it on Canadian defenseman Ryan Murray.
The Montreal Canadiens, picking third, grabbed Yakupov's compatriot and Sting team mate centre Alex Galchenyuk before the focus shifted back to defensemen with a record eight blueliners taken in the first 10 selections.
Picking fourth, the New York Islanders started a run of seven consecutive defensemen taking Griffin Reinhart, whose father Paul was a first round selection in 1979, while the Toronto Maple Leafs went for Morgan Reilly at number five.
The first round also featured a major trade with the Pittsburgh Penguins shipping centre Jordan Staal to the Carolina Hurricanes for Brandon Sutter, defenseman Brian Dumoulin and the eighth overall selection, which they used on Canadian defenseman Derrick Pouliot.
Staal, who turned down a 10-year $60 million contract extension earlier in the week, learned he was joining his brother Eric in Carolina on his wedding day.
"As an organisation we just thought it was the right thing to do for Jordan, he's ready for an expanded role and Carolina is certainly a great place for him," Penguins general manager Ray Shero. "He had a wonderful six years here.
"It was a good return for us."
The draft continues on Saturday with rounds two through seven.
The following are the top 10 picks from the NHL entry draft.
1. Edmonton Oilers, Nail Yakupov (Russia), right wing
2. Columbus Blue Jackets, Ryan Murray (Canada) defense
3. Montreal Canadiens, Alex Galchenyuk (Russia) centre
4. New York Islanders, Griffin Reinhart (Canada) defense
5. Toronto Maple Leafs, Morgan Reilly (Canada) defense
6. Anaheim Ducks, Hampus Lindholm (Sweden) defense
7. Minnesota Wild, Matt Dumba (Canada) defense
8. Pittsburgh Penguins (from Carolina Hurricanes), Derrick Pouliot (Canada) defense
9. Winnipeg Jets, Jacob Trouba (United States) defense
10. Tampa Bay Lightning, Slater Koekkoer (Canada) defense