From the official NHL release:
ORDER OF SELECTION FOR THE 2016 NHL DRAFT
The 2016 NHL draft will be held June 24-25 at First Niagara Center in Buffalo, N.Y. The first round will start at 7 p.m. ET Friday; rounds 2-7 will be held Saturday beginning at 10 a.m. ET.
Round 1
1. Toronto
2. Winnipeg
3. Columbus
4. Edmonton
5. Vancouver
6. Calgary
7. Arizona
8. Buffalo
9. Montreal
10. Colorado
11. New Jersey
12. Ottawa
13. Carolina
14. Boston
15. Minnesota
16. Detroit
17. Nashville
18. Philadelphia
19. NY Islanders
20. Arizona (from NYR)
21. Carolina (from LAK)
22. Winnipeg (from CHI)
23. Florida
24. Anaheim
25. Dallas
26. Washington
27. Tampa Bay
28. St. Louis
29. Boston (from SJS)
30. Toronto (from PIT)
Round 2
31. Toronto
32. Edmonton
33. Florida (from VAN)
34. Columbus
35. Calgary
36. Winnipeg
37. Arizona
38. Buffalo
39. Montreal
40. Colorado
41. New Jersey
42. Ottawa
43. Carolina
44. Tampa Bay (from BOS)
45. Montreal (from MIN via BUF)
46. Detroit
47. Nashville
48. Philadelphia
49. Boston (from NYI)
50. Chicago (from NYR via CAR)
51. Los Angeles
52. Philadelphia (from CHI)
53. Arizona *
54. Calgary (from FLA)
55. Pittsburgh (from ANA via VAN)
56. Calgary (from DAL)
57. Toronto (from WSH)
58. Tampa Bay
59. St. Louis
60. San Jose
61. Pittsburgh
* compensatory pick - ARI did not sign 2014 1st-round pick Conner Bleackley (acquired in trade with COL)
Round 3
62. Toronto
63. Edmonton
64. Vancouver
65. Columbus
66. Calgary
67. Carolina (from WPG)
68. Arizona
69. Buffalo
70. Montreal
71. Colorado
72. Toronto (from NJD via PIT)
73. New Jersey (from OTT)
74. Carolina
75. Carolina (from BOS)
76. Buffalo (from MIN via FLA, NJD, ANA)
77. New Jersey (from DET)
78. Nashville
79. Philadelphia
80. Ottawa (from NYI)
81. NY Rangers
82. Philadelphia (from LAK)
83. Chicago
84. Edmonton (from FLA)
85. Anaheim
86. Buffalo (from DAL)
87. St. Louis (from WSH)
88. Tampa Bay
89. Buffalo (from STL)
90. Dallas (from SJS)
91. Edmonton (from PIT)
Round 4
92. Toronto
93. Anaheim (from EDM)
94. Florida (from VAN)
95. Chicago (from CBJ)
96. Calgary
97. Winnipeg
98. NY Rangers (from ARI)
99. Buffalo
100. Montreal
101. Toronto (from COL)
102. New Jersey
103. Ottawa
104. Carolina
105. New Jersey (from BOS)
106. Minnesota
107. Detroit
108. Nashville
109. Philadelphia
110. NY Islanders
111. San Jose (from NYR)
112. Los Angeles
113. Chicago
114. Florida
115. Anaheim
116. Dallas
117. Washington
118. Tampa Bay
119. St. Louis
120. San Jose
121. Pittsburgh
Round 5
122. Toronto
123. Edmonton
124. Montreal (from VAN)
125. St. Louis (from CBJ)
126. Calgary
127. Winnipeg
128. Arizona
129. Buffalo
130. Buffalo (from MTL)
131. Colorado
132. New Jersey
133. Ottawa
134. Carolina
135. Boston
136. Boston (from MIN)
137. Detroit
138. Nashville
139. Philadelphia
140. Vancouver (from NYI via FLA)
141. NY Rangers
142. Los Angeles
143. Chicago
144. Chicago (from FLA)
145. Washington (from ANA via TOR)
146. Dallas
147. Washington
148. Tampa Bay
149. Edmonton (from STL)
150. San Jose
151. Pittsburgh
Round 6
152. Toronto
153. Edmonton
154. Vancouver
155. Columbus
156. Calgary
157. Winnipeg
158. Arizona
159. Buffalo
160. Montreal
161. Colorado
162. New Jersey
163. Ottawa
164. Carolina
165. Boston
166. Calgary (from MIN)
167. Detroit
168. Nashville
169. Philadelphia
170. NY Islanders
171. NY Rangers
172. Philadelphia (from LAK)
173. Chicago
174. Florida
175. Florida (from ANA)
176. Dallas
177. Washington
178. Tampa Bay
179. Toronto (from STL)
180. San Jose
181. Pittsburgh
Round 7
182. Toronto
183. Edmonton
184. Vancouver
185. Columbus
186. Calgary
187. Winnipeg
188. Arizona
189. Buffalo
190. Buffalo (from MTL)
191. Colorado
192. New Jersey
193. NY Islanders (from OTT)
194. Vancouver (from CAR)
195. Boston
196. Minnesota
197. Detroit
198. Nashville
199. Philadelphia
200. NY Islanders
201. NY Rangers
202. Los Angeles
203. Chicago
204. Minnesota (from FLA)
205. Anaheim
206. Tampa Bay (from DAL via EDM)
207. Washington
208. Tampa Bay
209. St. Louis
210. San Jose
211. St. Louis (from PIT)