New Jersey earned the second overall selection, while Arizona will pick third.
The Canadiens haven't picked first since 1980 when center Doug Wickenheiser was selected from the WHL's Regina Pats.
Previous first overall picks in franchise history include Guy Lafleur (1971), Réjean Houle (1969), Michel Plasse (1968) and Garry Monahan (1963).
"It's exciting for us as a management group, and it's certainly exciting for us as an organization. I remember the last time the Draft was in Montreal. It was a packed house. That isn't the case in every Draft location, so especially with us owning the first pick, I can only imagine the buildup of anticipation, excitement and interest in the Montreal Canadiens," said general manager Kent Hughes. "You hope as an organization that you don't pick number one overall too often, but when you're in that situation, it's pretty special."