A first-half hat-trick from star striker Ada Hegerberg followed an early opener by Germany captain Dzsenifer Marozsan to hand the French giants their sixth title overall.
A late strike by Asisat Oshoala was scant consolation for first-time finalists Barca who were bidding to become the first club to win Champions League honours with both their men's and women's teams.
The final was settled by the half-hour as Barca were swiftly overwhelmed by Reynald Pedros's powerful, slick-passing side inspired by inaugural Ballon D'Or winner Hegerberg.
"This is an incredible night for me personally, scoring a hat-trick in a Champions League final," the 23-year-old Norwegian, who was later named Player of the Match, told reporters.
"Everybody was at their top level today, we were ready on the pitch, you could feel that from minute one," she said.
Watch out for Barcelona in 'historic' women's final, warns Lyon star Bronze
Pedros stressed that Lyon's stellar performance, especially in the first half, was a "collective effort".
"Ada played an awesome game today as the rest of the team did, she just finished her teammates' work, which is what we expect from her," he said.
Budapest-born midfielder Marozsan, cheered throughout by local fans in the packed 22,000-capacity Ferencvaros Stadium, set Lyon on their way after just five minutes.
The 27-year-old turned a Shanice van de Sanden cross past Barcelona goalkeeper Sandra Panos, triggering chants of "Hungaria-Hungaria!" from the stands.
Then Lyon's chief executioner Hegerberg put Barcelona to the sword with a quick-fire treble to delight their travelling support of around 500.
Her first arrived on 14 minutes when she exploited slack Barcelona marking to tap in another van de Sanden pass from the right flank.
Five minutes later, again unmarked in the box, the tall striker was fed this time from the left by Amel Majri and clinically finished past the hapless Panos.
Then on the half-hour an in-swinger from English right-back Lucy Bronze evaded a despairing Panos lunge to reach the Norwegian who side-footed home her third, and Lyon's fourth.
"The goals came from similar situations down the wings that we had worked on and prepared the week before the game," said Pedros.
Shellshocked Barcelona, who had not conceded a goal in six Champions League ties before the final, even squandered a lifeline seconds before half-time when Alexia Putellas headed over a glorious chance from a corner.
Lyon, rampant in the first half, eased up in the second although they nearly extended their lead when Eugenie Le Sommer fired just over on 50 minutes after running onto a Marozsan backheel.
Luis Cortes's team managed to gradually create chances and a lob from captain Vicky Losada that shaved the bar 15 minutes from the end almost produced a consolation goal for Barcelona.
That eventually came in the last minute when substitute Oshoala, the first Nigerian to play in a Champions League final, calmly slotted home from the edge of the area.
But for all-conquering Lyon, whose European title complements an unbeaten domestic double-winning season, victory in the Hungarian capital was never in doubt.
"Lyon is just too far ahead of everybody. They have the best players in every position," said Cortes, whose side was the first Spanish team to reach the women's Champions League final.
"The message that we have to take home with us is that we beat Lyon in the second half, and that we have to play at the same level for 90 minutes," he said.
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