The draft will be held June 24-25 at First Niagara Center in Buffalo.
Five teams have multiple picks in the first round.
The Winnipeg Jets, who won the second pick in the lottery, also have the Chicago Blackhawks' pick at No. 22, acquired in the trade for forward Andrew Ladd.
The Arizona Coyotes have the seventh pick and the New York Rangers' selection at No. 20, acquired in the trade for defenseman Keith Yandle.
The Carolina Hurricanes have their pick at No. 13 and the Los Angeles Kings' selection at No. 21, which they received in the trade for defenseman Andrej Sekera.
The Toronto Maple Leafs, who won the lottery and will pick No. 1, also have the Pittsburgh Penguins' pick from the Phil Kessel trade.
The Boston Bruins have the No. 14 pick and the Sharks' first-round selection, acquired in the trade for goaltender Martin Jones.
With the Penguins playing the Tampa Bay Lightning in the Eastern Conference Final and the Sharks opposing the St. Louis Blues in the Western Conference Final, those picks will be determined at the conclusion of the playoffs. The teams that lose in the conference finals will have the 27th and 28th picks. The losing team in the Stanley Cup Final will pick No. 29; the winner will have the 30th pick.
1. Toronto Maple Leafs
2. Winnipeg Jets
3. Columbus Blue Jackets
4. Edmonton Oilers
5. Vancouver Canucks
6. Calgary Flames
7. Arizona Coyotes
8. Buffalo Sabres
9. Montreal Canadiens
10. Colorado Avalanche
11. New Jersey Devils
12. Ottawa Senators
13. Carolina Hurricanes
14. Boston Bruins
15. Minnesota Wild
16. Detroit Red Wings
17. Nashville Predators
18. Philadelphia Flyers
19. New York Islanders
20. Arizona Coyotes (from New York Rangers)
21. Carolina Hurricanes (from Los Angeles Kings)
22. Winnipeg Jets (from Chicago Blackhawks)
23. Florida Panthers
24. Anaheim Ducks
25. Dallas Stars
26. Washington Capitals
