The announcement was made by Hockey Canada president and CEO Tom Renney at a news conference in Toronto.
Armstrong's assistants include three fellow NHL general managers — Marc Bergevin (Montreal), Ken Holland (Detroit) and Bob Murray (Anaheim).
Los Angeles Kings assistant GM Rob Blake was also named to the staff, along with Hockey Canada executive Scott Salmond.
Armstrong just completed his fifth season at the helm of a Blues team that won the Central Division before losing in the first playoff round to Minnesota. He was part of the management team for the Canadian squads who won Olympic gold in 2010 and 2014.
The World Cup of Hockey takes place from Sept. 16 to Oct. 1, 2016 in Toronto, and will feature NHL players representing the "big six" hockey countries — Canada, the United States, Russia, Sweden, Finland and the Czech Republic.
There will also be two mixed-nationality teams — one composed of Europeans, the other of North American players under 23 years old. In order to help fill out that roster, North Americans who are under 23 are ineligible to play for their national teams.