Gallagher was named to one of three forward spots on the team, along with Chicago Blackhawks left-winger Brandon Saad and Florida Panthers centre Jonathan Huberdeau.
All three were finalists for the Calder Trophy as the NHL's top first-year player, won by Huberdeau.
Saad picked up a nice consolation prize, though, hoisting the Stanley Cup earlier this month with the Blackhawks.
Schultz was joined on the defence by Jonas Brodin of the Minnesota Wild. The top rookie netminder was Jake Allen of the St. Louis Blues.
The All-Rookie Team was chosen by members of the Professional Hockey Writers' Association, who voted at the end of the regular season.