Rogic pulled the strings in midfield with a composed performance, and opened the scoring for Celtic in the 16th minute, after cutting onto his left foot and bending the ball past Joe Lewis.
The Socceroos midfielder then turned provider in the 37th minute, picking out James Forrest who doubled the Hoops' advantage before halftime.
Moussa Dembele put the icing on the cake from the penalty spot after Anthony O'Connor brought down Forrest in the box and Dembele stepped up to the penalty spot and sent Joe Lewis the wrong way.
Celtic's 100th major trophy was also Brendan Rodgers's first piece of silverware as a manager, and the former Liverpool boss already has his sights set on winning the next trophy.
"That is what the great history of this club is based upon," Rodgers said.
"It makes the milestone, that century of trophies over the course of history.
"And now we have to look to the next one and start the next century of trophies and that will be important for the club
"But for now it is a great night for the Celtic supporters to celebrate, they must have enjoyed the performance and, as I say, we push for the next one."
Rogic was delighted with Celtic's performance and hailed his team-mates for their hard work leading up to the match.
"I think the fans deserve it, we deserve it as the playing squad because we have worked hard all season - it's no less than we deserve," Rogic said.
"We won 3-0 but it's not easy against Aberdeen. They have pushed us very close in the last few years but I feel this season we have gone up a level, but there are days like this that you enjoy playing football."