Career
He is currently playing with the Chicago Wolves of the American Hockey League (AHL) while under contract to the Saint Louis Blues of the National Hockey League (National Hockey League). Veilleux was selected by the Blues in the 4th round (102nd overall) of the 2011 National Hockey League Entry Draft. Veilleux was selected second overall by Shawinigan Cataractes in the 2009 QMJHL Entry Draft.
On March 6, 2013, the Saint Louis Blues signed Veilleux to a three-year, entry-level contract.