New York acquired the No. 26 pick from the Boston Bruins as part of the Rick Nash trade on Feb. 25.
The 2018 draft is at American Airlines Center in Dallas. The first round is June 22, and rounds 2-7 are June 23.
The first 15 selections were set by the NHL Draft Lottery, which was held April 28. The Buffalo Sabres won the lottery and have the No. 1 pick, followed by the Carolina Hurricanes and the Montreal Canadiens.
Picks 16-27 were set following the completion of the conference semifinals, based on inverse order of the NHL standings.
The Lightning, as the losing team in the conference finals with the fewest regular-season points, were assigned the 28th pick.
The St. Louis Blues have the 29th pick. They acquired the selection from the Winnipeg Jets, who lost to the Vegas Golden Knights in the Western Conference Final, as part of the trade for center Paul Stastny on Feb. 26.
The Blues have only that selection in the first round. They traded their first-round pick (No. 14) to the Philadelphia Flyers as part of the trade to acquire forward Brayden Schenn on June 23, 2017.
The Stanley Cup champion will get the No. 31 pick, with the losing team in the Cup Final getting No. 30.
Vegas' pick belongs to the Detroit Red Wings, who acquired it in a trade for forward Tomas Tatar on Feb. 26.
Here is the updated first-round order:
1. Buffalo Sabres
2. Carolina Hurricanes
3. Montreal Canadiens
4. Ottawa Senators
5. Arizona Coyotes
6. Detroit Red Wings
7. Vancouver Canucks
8. Chicago Blackhawks
9. New York Rangers
10. Edmonton Oilers
11. New York Islanders
12. New York Islanders (from Calgary Flames)
13. Dallas Stars
14. Philadelphia Flyers (from St. Louis Blues)
15. Florida Panthers
16. Colorado Avalanche
17. New Jersey Devils
18. Columbus Blue Jackets
19. Philadelphia Flyers
20. Los Angeles Kings
21. San Jose Sharks
22. Ottawa Senators (from Pittsburgh Penguins)
23. Anaheim Ducks
24. Minnesota Wild
25. Toronto Maple Leafs
26. New York Rangers (from Boston Bruins)
27. Chicago Blackhawks (from Nashville Predators)
28. New York Rangers (from Tampa Bay Lightning)
29. St. Louis Blues (from Winnipeg Jets)
30. Stanley Cup Final runner-up
31. Stanley Cup champion
