On a sweltering evening in central London this week, smartly dressed young women gathered to discuss "Redefining Success Beyond Money and Power". The keynote speaker contrasted the ancient Greek philosophers' ideal of "a good life" with our modern misapprehension that it means working 24/7, sleepless and stressed, soldered to a BlackBerry. We need a revolution to redefine success, she told her audience. Rest, relaxation and meditation are the future. "Prioritise your health. Live your life as if everything is rigged in your favour. Burnt-out people do not create a sustainable planet."

She could pass quite easily for the owner of a wellbeing centre for Notting Hill ladies who lunch. Regally coiffed and impeccably dressed, she said nothing much that you won't already have heard from yoga enthusiasts. The surprise is that she is one of the most powerful media moguls in the world.

We meet the following day at the offices of Huffington Post UK, one of eight global offices (with more to open shortly) producing one of the most popular English language news website on the planet. Created in 2005, its eclectic mix of original journalism, links to other published articles and blogs by anyone from Barack Obama to a homeless teenager is now read by more than 75 million people every month, and was bought by AOL two years ago for $315m.

Arianna Huffington has been confounding expectations ever since she arrived in London from Greece as a 16-year-old with her mother and sister, saw a photo of Cambridge University and decided to apply. With the exception of her mother – "my rock of Gibraltar" – everyone told her she didn't stand a chance, not least because she could barely speak English. She won a place to study economics, joined the union, got laughed at for her accent and total ignorance of the rules of debating, but was elected its first foreign female president. She was soon appearing on TV panel shows, fell in love with the celebrated Times columnist Bernard Levin and published her first bestseller – a riposte to Germaine Greer's Female Eunuch – at 23. By 30 her fourth book had been serialised in the Sunday Times for a record-breaking £150,000. But when Levin, twice her age, refused to marry and have children, off she went with her mother and sister to conquer New York.

Soon she was Manhattan's premiere socialite, and before long an oil billionaire's wife. Relocating to Washington in the 80s, she became the darling of the Republican right, getting her husband elected to Congress and establishing herself as a glamorous DC power broker. After 11 years and two daughters, the marriage ended amicably after his announcement that he was bisexual, prompting another move – to California, mother and sister still in tow – where she reinvented herself again as a passionate liberal and society queen. She ran against Arnold Schwarzenegger for state governor in 2003, before drawing on 40 years of high-octane networking to get her rich and famous friends to fund and write for Huffpost, which she describes as her "last act" and the realisation of her life's work and dreams. "Everything," as she puts it happily, "happens for a reason."

How has she managed to pull all this off? The snobbery and sexism in elite circles towards someone who boasts of being of "Greek peasant stock" and sounds not unlike Clive James' old novelty sidekick, Margarita Pracatan, scarcely bears thinking about. People who know Huffington cite her charm as the answer – so I ask her to demonstrate. The first clue is a sheaf of papers in her hand, which she was skimming as she arrived, and which are her research notes on me. This, I can safely say, has never happened before. She mentions articles I've written, and tells me she's ordered a book I wrote years ago. "I love the title," she purrs. "I love it. I think I'm going to learn a lot about you."

Let's pretend I'm a powerful political player she's just met at a cocktail party, I suggest. What would she say to me? She dissolves into bashful giggles. "For me it is about how good a listener you are. How you listen. Because the worst thing you can do in terms of connecting with people is when you are looking over their shoulder to see if there is someone more interesting in the room. And I think what we all want is to be seen in a real way. To really be present."

She never bothers discussing current affairs. "Few people have really profound thoughts on the news of the day, right? They're just rehashing whatever the editorial said. I want to talk to people about themselves. What's happening in their lives. And I think that's what people really talk about. I'm much more interested in having real conversations. I would want to talk to you about how you dealt with your mother's death, or about your book."

She claims not to deploy flattery, though I suspect she's not averse to a bit now and then. The real secret seems to be her astonishing resilience in the face of criticism or failure. "I think you have to understand – you have to think of my mother. She was an incredible force in my life because she'd given me this amazing, unconditional love, which was like a treasure trove, so whatever else was going on I felt this incredible loving from her. The feeling she brought me and my sister up on was: try, whatever it is; failure is not the opposite of success but a stepping stone to success. So if you stand up at the Cambridge union and they ridicule you, it doesn't matter; you'll stand up again and you'll learn and get better at it." She used to replay humiliations over and over in her head. "But my mother would say: 'Change the channel, darling.'" Huffington's name for self criticism is "the obnoxious flatmate in my head", whom she appears successfully to have evicted.

Her latest big idea is a movement she calls The Third Metric and describes as "the third wave of feminism", which may come as a surprise to all the feminists who thought they'd launched the third wave some time around 1990. "What we're saying is we need to reshape the world in which women are participating. Not just break through ceilings in the current broken system. We have to get away from the way men have constructed work around war metaphors and sports metaphors and praising each other for working 24/7, working round the clock – these phrases simply encourage a very destructive way to lead our lives, and we are paying a very high price."

She cites Steve Jobs and Bill Gates, whose best ideas apparently came after meditating or retreating to a technology-free log cabin. "We must learn to really think and connect with our wisdom, and I really believe we all have that deeper wisdom in us." But the government keeps saying the problem is that we've grown much too lazy. If we want to compete with the emerging economies, don't we all have to become like South Koreans?

"Well look at the rate of suicide in South Korea, look at the price they are paying for the way that they work. We launched in Japan recently, and there's a whole literature that emerged because the way the Japanese worked didn't help the economy. I read a piece in the New York Times by the former CFO of Lehman Brothers, and she described her life, working round the clock, no personal life, she destroyed her marriage, paid a heavy price. And I kept thinking all the time: but you weren't even a good CFO. Or you would have noticed that there was an iceberg about to hit Lehman Brothers. So my point is, it's not a trade-off: either you work really hard and are successful, or not. We are seeing that mindfulness and meditation are all also performance-enhancement techniques."

Huffington has always had a thing for new age ideas – she dabbled in the 70s encounter group movement, and tried neuro-linguistic programming – but when I ask if the Third Metric is the latest incarnation of that interest she looks slightly put out. "I would say that the great thing today is we have so much scientific evidence about how the Third Metric ideas work. 'New age' – it's flakey, it feels speculative. This is based on hardcore science. A lot of the ideas are the same, you're absolutely right – ever since I was a little girl it's taken many forms but it's part of the same search for transcendence, for meaning. And this has been a big part of my life as a quest, if you like. But people are really open to these ideas in a way that they weren't. There's a very different interest now. And part of it is all these new scientific findings that have made such a difference in how all these ideas are presented. I love reading all the latest scientific findings." Her reverence about science is palpably sincere, but can sound a bit excitably credulous. "I just love what the Dalai Lama's doing," she adds. "He has partnered with neuroscientists in Madison, Wisconsin," which must be about as perfect a conflation as Huffington could ever wish for.

Lots of journalists would love to stop working 24/7, but blame websites including the Huffington Post for taking their work and giving it away for free. She looks puzzled. "I'm surprised because that's such a discredited argument. I'm a big believer in aggregation, but we always link back to the creators, so he or she would have a lot more traffic for their work. Beyond that, the Huffington Post has 800 jobs for journalists, editors and engineers, so that argument is really obsolete." She says staff pay is comparable to newspaper rates, though as I don't see anyone in the office who looks much over 25, I doubt it amounts to much. Some bloggers who had been happy to write for Huffington for free took exception to enriching AOL's corporate coffers, but "that argument lasted for about 48 hours" she says dismissively, and offers a persuasive analogy. People are happy to talk about their ideas on Newsnight for free, she points out; she's merely offering them a global platform.

Huffington is an immensely likable conundrum: a curious mixture of inspired insights and really quite banal observations. But they are certainly no less original than those of most highflying men, and the fact that her politics have shifted so radically from right to left helps to make them interesting by the mere fact of how far they have changed. The irony of a media mogul who famously owns three BlackBerrys now evangelising for a more relaxed working culture should be hilarious but, ever the maestro of reinvention, she says that since fracturing her cheekbone by falling asleep on her keyboard in 2007 she has in fact transformed her own working life. "I now sleep seven to eight hours – before it was four to five. That makes a huge difference, in everything – not just my health and my wellbeing, but also my decision-making. I have more clarity, I can make better and faster decisions, I'm less reactive."

At 63 she is a multimillionaire, her daughters are grown up and she cannot think of a single famous living person she would like to meet but has not. By any definition of success, she has surely reached the point at which she could stop, hasn't she?

"But what else would I be doing? I'd be bored to death lying on a beach in the south of France."