Gillies was selected by the Calgary Flames in the third round (No. 75) of the 2012 NHL Draft. His grandfather, Bruce Gillies Sr., played at Norwich University. His father, Bruce Gillies, is a member of the University of New Hampshire Hall of Fame and helped Muskegon of the United States Hockey League win the Turner Cup in 1985-86.
Jon Gillies played three seasons at Providence of Hockey East and started for the United States at the 2014 IIHF World Junior Championship. As a junior, Gillies helped Providence win the NCAA Championship by going 24-13-2 with a 2.01 goals-against average and .930 save percentage. He was named the Most Outstanding Player in the Frozen Four.