The Cats fielded the oldest team in the league's 126-year history on Saturday but were full of running in a 20.13 (133) to 8.4 (52) victory in front of 100,024 fans at the MCG.
It was the first decider at the home of football in three years after two seasons affected by the global pandemic.
The Cats' 10th flag was their second under Chris Scott and first since 2011, following a heartbreaking run of five preliminary final defeats and a grand final loss two years ago.
"They're so hard to win," Geelong captain Joel Selwood told the Seven Network.
"Every side says it, but I think we deserved one. (We've) just been bashing away.
"We don't apologise for being up there, having a crack at it each year ... this has been built over five or six years."
Isaac Smith (32 disposals, three goals), Patrick Dangerfield (26 disposals), Tom Hawkins (three goals) and Mark Blicavs (23 disposals) were all outstanding - and all among the 10 Cats aged 30 years or older - while young defender Sam De Koning shone in the back half.
Small forward Tyson Stengle, who was axed by Adelaide after off-field indiscretions, completed his remarkable redemption story with four goals.
Selwood (26 disposals, one goal) was influential in his record-breaking 40th finals appearance.
Dangerfield became the second player in history to win his first premiership after playing more than 300 games.
"This is Everest. This is the pinnacle. This is what it means to be content, I think," Dangerfield told the Seven Network.
"It was worth the wait and better than I ever could have ever imagined. It's bloody special.
"We've sort of been able to enjoy it because we just played such a complete game.
"It always felt like we'd been building throughout the year and I think it culminated in today."
Most of Sydney's guns failed to fire and the selection gamble on Sam Reid backfired spectacularly when he was substituted out because of the adductor injury he carried into the game.
Chad Warner (29 disposals, 10 clearances, two goals) and Luke Parker (23 disposals, 14 tackles) were the Swans' best, while superstar forward Lance Franklin was kept goalless by Jack Henry.
Minor premiers Geelong entered the grand final as hot favourites on a 15-game winning streak.
Hawkins gave them a quick start when he kicked the first two goals of the match in identical fashion, out-muscling Swans ruckman Tom Hickey at boundary throw-ins and snapping truly.
Smith also kicked two early majors as the Cats piled on six in the opening term to take a commanding 35-point lead by quarter-time.
It was the biggest margin at that stage of a grand final since 1989.
Geelong's pressure was immense and Sydney wilted.
The result was put to bed early in the second half, when two Tom McCartin errors deep in defence led directly to Geelong goals.
McCartin was first caught holding the ball by Mitch Duncan and then had a kick across the back-line intercepted by Brad Close.
Smith's third major moments later blew the margin out to 54 points and the Cats were never in danger from there as Sydney posted their lowest score of the season.
There was heartbreak before the bounce for Geelong youngster Max Holmes, who was deemed too big a selection risk because of doubts over his hamstring.
Mark O'Connor replaced Holmes and joined Zach Tuohy as the first Irishmen to win an AFL premiership since Sydney's trailblazing Tadgh Kennelly in 2005.
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