The Calgary Flames picked defenseman Carson Carels sixth overall, and the Winnipeg Jets selected Swedish center Viggo Bjorck eighth overall.
"Just to be here, it's a privilege," Bjorck said. "And then go top-10 to Winnipeg, a very hockey-culture city, it's really special."
Vancouver also selected Adam Novotny at number 24.
Ottawa chose Jonas Lagerberg Hoen at 25, Montreal traded up for Gleb Pugachyov at 26, Calgary added Jack Hextall at 30, and Ottawa concluded with Jaxon Cover at 32.
Cover, an 18-year-old from Grand Cayman, transitioned to ice hockey later in life after starting as an in-line player.
"If you really, truly do love something, you don't need to play it your whole life," Cover said.
"I want to teach kids from unconventional places that even though you're from an unconventional place, you could still play a sport that you love."
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Development camps and player evaluations for the newly drafted prospects are scheduled to begin in the coming weeks.