Canadian heart-throb Bieber, fresh from breaking up with his girlfriend of two years, Selena Gomez, scooped Best Male Artist for the third year in a row, with millions of fans voting to name the winners.
Bieber, 18, who did not attend the ceremony in the western German city of Frankfurt, also bagged Best Pop Act and Best World Stage Performance.
Swift of the US claimed the gong for Best Female Artist from presenter Lana Del Rey as the show got underway and went on to pick up honours for Best Live Act and Best Look.
"This is my very first EMA -- I'm so excited," said the 22-year-old blonde, who later dressed up as a circus ringleader to perform her hit "We Are Never Ever Getting Back Together" in the show's finale.
"This was our first European tour -- thank you for giving me one more amazing reason to come back and see you."
Psy, whose single "Gangnam Style" has more than 700 million views on YouTube and spawned countless videos copying his signature horse-riding dance, paid tribute to his wife of six years and loved ones back home when he picked up his award.
"I'd like to thank all my family who's got to live with a selfish job, with a selfish guy," the 34-year-old quipped.
Han Geng of China beat out Rihanna for Best Worldwide Act, awarded for only the second time. The 24-year-old Barbadian beauty, who had led with six nominations, went home empty-handed, as did flamboyant US trailblazer Lady Gaga, who was up for three awards.
Del Ray claimed Best Alternative Act and Nicki Minaj won for Best Hip Hop.
The Best Song prize went to Canada's Carly Rae Jepsen for the catchy "Call Me Maybe", which she collected from US reality show star Kim Kardashian.
"All I can say is I was not expecting this," she said as she hoisted the statuette, a globe topped with a wobbling MTV logo on a spring.
Jepsen, 26, thanked Bieber, who set her song on its trajectory by promoting it online.
German-born supermodel Heidi Klum, 39, hosted the show, and made her entrance at the century-old Festhalle, decorated for a circus tent theme, in a sexy bridal gown and jaunty black top hat. She sat perched on a trapeze as the prize handout began.
Kardashian had a minor wardrobe malfunction when she came on stage as a spike heel got caught in the train of her low-cut black Stephane Rolland gown, leading her to stumble.
"I'm clumsy," she later joked backstage.
US soul singer Alicia Keys led a tribute to Whitney Houston, as Beyonce lent a voice-over to a video in honour of the late US singer. A further shout-out went to Beastie Boy Adam Yauch, who died of cancer in May.
The MTV Europe Awards are held each year in a different European city, with past hosts including Belfast in 2011, Madrid in 2010 and Berlin in 2009.
The show featured a few innovations this time, with "Knight Rider" and "Baywatch" star David "The Hoff" Hasselhoff serving as the show's "social media correspondent" and offering live commentary on Twitter and joining Psy for a cameo during his live performance.
British newcomer Rita Ora opened the show with a spectacular pyrotechnic-studded performance of her hit "R.I.P", followed by acts including US indie band fun, No Doubt, Jepsen, Keys and Las Vegas rockers The Killers.
AFP
Mon Nov 12 2012
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