Demko was selected by the Vancouver Canucks in the second round (No. 36) of the 2014 NHL Draft following his freshman season at Boston College, where he went 16-5-3 with a 2.24 goals-against average and a .919 save percentage.
In three seasons with the Eagles, Demko was 62-26-10 with a 2.08 GAA and .928 save percentage. He helped Boston College advance to the NCAA Frozen Four twice (2014, 2016), was a finalist for the 2016 Hobey Baker Award and won the Mike Richter Award as the NCAA's most outstanding goaltender in 2016. His 10 shutouts in 2015-16 are a Boston College record and is the second most in college hockey history for a single season.