Gillies made 49 saves for Providence in a 4-3 win over Boston University on Saturday to end his college career with an NCAA championship.
The 6-foot-6, 225-pound goalie from South Portland, Maine, was the Most Outstanding Player of the Frozen Four tournament.
Calgary drafted Gillies 75th overall in the third round of the 2012 draft.
Gillies joined the Flames for a pregame skate in Vancouver on Wednesday prior to Game 1 of their first-round playoff series against the Canucks.
He had a goals-against average of 2.01 and a save percentage of .930 in 38 games for Providence this past season.
In three seasons with the Friars, Gillies had a 60-34-13 record with 13 shutouts. His career GAA was 2.08 and his save percentage was .931.