Gibson was born and raised in Finland before he moved to Saskatchewan at age 15 to attend Notre Dame College. In his first season, he helped the midget AAA team win the Telus Cup national championship. He was selected by Chicoutimi of the Quebec Major Junior Hockey League as the No. 1 goaltender in the 2009 Canadian Hockey League import draft.
Gibson was selected in the second round (No. 49) by the Los Angeles Kings in the 2011 NHL Draft. But after playing two more seasons with Chicoutimi, he did not sign with the Kings and signed with the Toronto Maple Leafs on July 19, 2013.