Calgary drafted Gillies 75th overall in the third round of the 2012 NHL entry draft.
Gillies, 21, made 49 saves for Providence in a 4-3 win over Boston University on Saturday to cap his college career with an NCAA championship.
The six-foot-six, 225-pound goalie from South Portland, Maine, was named the most valuable player of the Frozen Four tournament.
Gillies joined the Flames for a pre-game skate in Vancouver on Wednesday prior to Game 1 of their first-round playoff series against the Canucks.
He posted a goals-against average of 2.01 and a save percentage of .930 in 38 games for Providence College this past season.
In three seasons with the Friars, Gillies posted a 60-34-13 record with 13 shutouts. His career GAA was 2.08 and his save percentage was .931.
Also Wednesday, Calgary sent Finnish goaltender Joni Ortio to the Adirondack Flames of the American Hockey League.
In six games with Calgary this season, Ortio has a 4-2-0 record with one shutout, a 2.52 GAA and a .908 save percentage.
Note to readers: This is a corrected story. A previous version incorrectly stated the Frozen Four title game was Sunday.