Gregoris Tsahas has smoked a packet of cigarettes every day for 70 years. High up in the hills of Ikaria, in his favourite cafe, he draws on what must be around his half-millionth fag. I tell him smoking is bad for the health and he gives me an indulgent smile, which suggests he's heard the line before. He's 100 years old and, aside from appendicitis, has never known a day of illness in his life.

Tsahas has short-cropped white hair, a robustly handsome face and a bone-crushing handshake. He says he drinks two glasses of red wine a day, but on closer interrogation he concedes that, like many other drinkers, he has underestimated his consumption by a couple of glasses.

The secret of a good marriage, he says, is never to return drunk to your wife. He's been married for 60 years. "I'd like another wife," he says. "Ideally one about 55."

Tsahas is known at the cafe as a bit of a gossip and a joker. He goes there twice a day. It's a 1km walk from his house over uneven, sloping terrain. That's four hilly kilometres a day. Not many people half his age manage that far in Britain.

In Ikaria, a Greek island in the far east of the Mediterranean, about 30 miles from the Turkish coast, characters such as Gregoris Tsahas are not exceptional. With its beautiful coves, rocky cliffs, steep valleys and broken canopy of scrub and olive groves, Ikaria looks similar to any number of other Greek islands. But there is one vital difference: people here live much longer than the population on other islands and on the mainland. In fact, people here live on average 10 years longer than those in the rest of Europe and America – around one in three Ikarians lives into their 90s. Not only that, but they also have much lower rates of cancer and heart disease, suffer significantly less depression and dementia, maintain a sex life into old age and remain physically active deep into their 90s. What is the secret of Ikaria? What do its inhabitants know that the rest of us don't?

The island is named after Icarus, the young man in Greek mythology who flew too close to the sun and plunged into the sea, according to legend, close to Ikaria. Thoughts of plunging into the sea are very much in my mind as the propeller plane from Athens comes in to land. There is a fierce wind blowing – the island is renowned for its wind – and the aircraft appears to stall as it turns to make its final descent, tipping this way and that until, at the last moment, the pilot takes off upwards and returns to Athens. Nor are there any ferries, owing to a strike. "They're always on strike," an Athenian back at the airport tells me.

Stranded in Athens for the night, I discover that a fellow thwarted passenger is Dan Buettner, author of a book called The Blue Zones, which details the five small areas in the world where the population outlive the American and western European average by around a decade: Okinawa in Japan, Sardinia, the Nicoya peninsula in Costa Rica, Loma Linda in California and Ikaria.

Tall and athletic, 52-year-old Buettner, who used to be a long-distance cyclist, looks a picture of well-preserved youth. He is a fellow with National Geographic magazine and became interested in longevity while researching Okinawa's aged population. He tells me there are several other passengers on the plane who are interested in Ikaria's exceptional demographics. "It would have been ironic, don't you think," he notes drily, "if a group of people looking for the secret of longevity crashed into the sea and died."

Chatting to locals on the plane the following day, I learn that several have relations who are centenarians. One woman says her aunt is 111. The problem for demographers with such claims is that they are often very difficult to stand up. Going back to Methuselah, history is studded with exaggerations of age. In the last century, longevity became yet another battleground in the cold war. The Soviet authorities let it be known that people in the Caucasus were living deep into their hundreds. But subsequent studies have shown these claims lacked evidential foundation.

Since then, various societies and populations have reported advanced ageing, but few are able to supply convincing proof. "I don't believe Korea or China," Buettner says. "I don't believe the Hunza Valley in Pakistan. None of those places has good birth certificates."

However, Ikaria does. It has also been the subject of a number of scientific studies. Aside from the demographic surveys that Buettner helped organise, there was also the University of Athens' Ikaria Study. One of its members, Dr Christina Chrysohoou, a cardiologist at the university's medical school, found that the Ikarian diet featured a lot of beans and not much meat or refined sugar. The locals also feast on locally grown and wild greens, some of which contain 10 times more antioxidants than are found in red wine, as well as potatoes and goat's milk.

Chrysohoou thinks the food is distinct from that eaten on other Greek islands with lower life expectancy. "Ikarians' diet may have some differences from other islands' diets," she says. "The Ikarians drink a lot of herb tea and small quantities of coffee; daily calorie consumption is not high. Ikaria is still an isolated island, without tourists, which means that, especially in the villages in the north, where the highest longevity rates have been recorded, life is largely unaffected by the westernised way of living."

But she also refers to research that suggests the Ikarian habit of taking afternoon naps may help extend life. One extensive study of Greek adults showed that regular napping reduced the risk of heart disease by almost 40%. What's more, Chrysohoou's preliminary studies revealed that 80% of Ikarian males between the ages of 65 and 100 were still having sex. And, of those, a quarter did so with "good duration" and "achievement". "We found that most males between 65 and 88 reported sexual activity, but after the age of 90, very few continued to have sex."

In a small village called Nas at the western end of Ikaria's north shore is Thea's Inn, a bustling guesthouse run by Thea Parikos, an American-Ikarian who returned to her roots and married a local. Ever since Buettner set up with his research team here a few years back, Thea's Inn has been a sort of base camp for anyone looking to study the island's older population.

It's a good introduction to Ikarian life, if only because the dining table always seems to bear a jug of homemade red wine and dishes made from garden-grown vegetables. Whatever household we enter over the next four days, even at the shortest notice, invariably produces the same appetising hospitality. Yet Ikarians are far from wealthy. The island has not escaped the Greek economic crisis and around 40% of its inhabitants are unemployed. Nearly everyone grows their own food and many produce their own wine.

There is also a strong tradition of solidarity among Ikarians. During the second world war, when the island was occupied by the Italians and Germans, there was substantial loss of life through starvation – some estimates put the death toll at 20% of the population. It's been speculated that one of the reasons for Ikarians' longevity is a Darwinian effect of survival of the fittest.

After the war, thousands of communists and leftists were exiled to the island, bringing an ideological underpinning to the Ikarians' instinct to share. As one of the island's few doctors told Buettner, "It's not a 'me' place. It's an 'us' place."

Nearly all elderly Ikarians have a story of suffering, though few are keen to tell it. Kostas Sponsas lost a leg in Albania, when he was blown up by a German shell. He was saved by fellow Ikarians, without whose help he would have died from loss of blood. "'Be strong,' they told me," he says. "'Have courage!'"

He turns 100 this month and is more mobile than many younger men with two legs. Each day he pays a visit to the office of the shop he set up decades ago. "If I feel tired, I read. It rests my mind."

He was determined not to get depressed after losing his leg as a young man, instead remembering his grandfather's advice. "He used to say to me, 'Be grateful that nothing worse has happened.'"

In terms of longevity, it was wise counsel. Depression, sadness, loneliness, stress – they can and do take a decade off our lives. Sponsas's own tips for a long life are that he never eats food fried with butter, always sleeps well and with the window open, avoids eating too much meat, drinks herb tea – mint or sage – and makes sure to have a couple of glasses of red wine with his food.

Sponsas's son, a large middle-aged man with a broad smile, is with him when I visit, fixing a broken door. Family is a vital part of Ikarian culture and every old person I visit has children and grandchildren actively involved in their lives. Eleni Mazari, an estate agent on the island and a repository of local knowledge, says, "We keep the old people with us. There is an old people's home, but the only people there are those who have lost all their family. It would shame us to put an old person in a home. That's the reason for longevity."

Sponsas agrees: "To have your family around you makes you feel stronger and more secure."

Just a minute's walk from his house in the picturesque port of Evdilos is the spotless home of Evangelia Karnava. In Ikaria, if you ask people their age, the answer they give is the year they were born. Karnava, a tiny but formidable woman, was born in 1916. She radiates a fierce energy, gesticulating like a politician on the stump. She lost two baby girls to starvation during the war but she's not someone haunted by tragedy. Instead, she speaks of her three children, seven grandchildren, four great-grandchildren and her great-great-grandchild. "I'm going to live to be 115," she tells me. "My grandmother was 107."

She certainly looks as if she's fit for a good few years yet. She cleans her own flat and goes shopping every day. What's her secret? She pours out glasses of Coca-Cola for her guests. "I can't live without it!" she says.

Buettner appreciates the irony. He has been studying the diets of the various "blue zones" he's visited for clues to a healthier lifestyle that can be transported to postindustrial western societies. Cigarettes and Coca-Cola were not meant to be part of the programme.

The phrase "blue zone" was first coined by Buettner's colleague, the Belgian demographer Michel Poulain. "He was drawing blue circles on a map in Sardinia and then referring to the area inside the circle as the blue zone," Buettner says. "When we started working together, I extended it to Okinawa, Costa Rica and Ikaria. If you Google it now, it's entered the lexicon as a demographically confirmed geographical area where people live measurably longer." So what does it take to qualify? "It's a variation," Buettner says. "It's either the highest centenarian rate, so the most centenarians per 1,000. Or it has the highest life expectancy at middle age."

All the blue zones are slightly austere environments where life has traditionally required hard work. But they also tend to be very social, and none more so than Ikaria. At the heart of the island's social scene is a series of 24-hour festivals, known as paniyiri, which all age groups attend. They last right through the night and the centrepieces are mass dances in which everyone – teenagers, parents, the elderly, young children – takes part. Kostas Sponsas tells me he no longer has the energy to go on until dawn. He will now usually take his leave by 2am.

One evening, the island's star violin player, whom we met at Gregoris Tsahas's favourite cafe, invites Buettner, me and several others back to his house to hear him play. He says he often grows exhausted while performing at festivals, but the energy and enthusiasm of the people keep him going. He plays some traditional folk tunes, full of passion and yearning and heart-rending beauty, and mentions with pride that Mikis Theodorakis, the composer of Zorba The Greek, was among the leftists exiled on the island in the late 1940s. Theodorakis later recalled the experience with pleasure. "How could this be?" he asked. "The answer is simple: it's the beauty of the island in combination with the warmth of the locals. They risked their lives to be generous to us, something that helped us more than anything bear the burden of the hardship."

One of the things Buettner has found that unites the elderly inhabitants of all the blue zones is that they are unintentionally old: they didn't set out to extend their lives. "Longevity happened to these people," he says. "The centenarians didn't all of a sudden at 40 say, 'I'm going to become 100; I'm going to start getting exercise and eating these ingredients.' It ensues from their surroundings. So my argument is that the environmental components of places such as Ikaria are portable if you pay attention. And the value proposition in the real world is maybe a decade more life expectancy. It's not living to 100. But I think the real benefit is that the same things that yield this healthy longevity also yield happiness."

I ask a number of men in their 90s and 100s if they do any keep-fit exercise. The answer is always the same: "Yes, digging the earth." Nikos Fountoulis, for example, is a 93-year-old who looks 20 years younger. He still has a smallholding in the hills of the island's interior. Each morning he goes out at 8am to feed his animals and tend his garden. He used to dig charcoal as a younger man. "I never thought about getting old," he says. "I feel good. I feel 93, but on Ikaria that's OK."

The island's greatest charm is that it is an unselfconscious sort of place. That could soon change: the spread of tourism is bound to have an effect. The island is protected by its remoteness and limited access, but is now at the mercy of blue zone tourists, those relentless hordes of blue-rinsed travellers looking for the secret elixir of eternal life. Buettner is doubtful that his book will lead to plane-loads of Floridian retirees crowding the island. "What are they going to do?" he asks. "They're not going to be able to descend upon the woman milking a goat."

On the day I leave Ikaria, I come across a man in a baseball cap sitting in a chair outside his house in Evdilos. He is called Vangelis Koutis and he's 97. He had left the island when he was 14 to join the merchant navy. He travelled all over the world, including Middlesbrough, and finally settled in Canada. But, like a lot of Ikarians, he decided to return home in later life, in his case when he was 70. I ask what brought him back.

"Fresh air," he says, "the best climate in the world and the friendliest people I've ever met."

With that, he returns to enjoying the sunshine on a beautiful spring afternoon. It's hard to imagine Middlesbrough, or many other places, offering quite so pleasant a time for a man in his 90s. Life in the blue zone is good. And that may be the real secret of why it's also so long.