In an eerie glade not far from Culloden, six tourists are picking their way across the mossy ground, the rain bouncing off their umbrellas like shrapnel, towards a rock which has been cleft in two.

Their guide, Hugh Allison, resplendent in Highland garb (though he later admits the kilt is by "McLidl"), has already explained the history of the Clava Cairns, a bronze age monument consisting of three burial chambers, each surrounded by a stone circle. Huddled together inside the first, the three couples - two from the US and one from England - listened spellbound as he explained how, at the winter solstice, the setting sun shines down the entrance passageway to the back of the chamber, as if lighting a path for the souls of the dead to travel from this world to the next.

But, as the leader of one of Scotland's first Outlander tours, Allison knows the split stone at the other end of the clearing is what everyone has come to see. If not exactly the inspiration for Craigh na Dun - the pagan site at the centre of the cult books and TV series, which are set and filmed in Scotland - Clava Cairns is accepted by author Diana Gabaldon and her fans as its real-life incarnation. Not only does its preternatural atmosphere lend itself to mystical imaginings, but the broken slabs which rise up like a crocodile's jaws are almost identical to those which consume the books' heroine, Claire Randall, transporting her through time from 1946 to the Jacobite era, where she falls in love with dashing outlaw Jamie Fraser.

Allison, owner of Inverness Tours, knows Gabaldon has given Clava Cairns her seal of approval because she has told him personally. Allison has driven the author round the north of Scotland; she has shared all sorts of titbits and anecdotes about her creative process. And when he decided to set up this tour, and was seeking out the best possible matches for the books' key locations - the Ord House Hotel in Muir of Ord for Lallybroch (the fictional seat of the Fraser clan); Castle Leod near Strathpeffer for Castle Leoch (the fictional seat of the Mackenzie clan) - he gave her power of veto over his plans. In the world of Outlander, where Gabaldon is a goddess and every snippet of inside info a precious commodity, this connection, which Allison is not shy of mentioning, is the source of much kudos.

Indeed, right now, he is reminding his party Gabaldon can be seen peering through the gap in these boulders in the photograph on the back of The Outlandish Companion, which helps readers keep track of the interlocking plots and characters. Thus briefed, the members of the group wander off to take their own photographs and swap observations. "In the book, the stone circle is up on a hill, but this one is on flat land," muses one. "I had imagined it simpler, like a much smaller Stonehenge, but it does have a pagan feel to it," says another. Pictures taken, everyone clambers aboard the people carrier again and we head for Culloden - scene of the final confrontation of the 1745 uprising - to learn about the slaughter that unfolded on Drumossie Moor and stand in front of the flower-strewn Clan Fraser stone, where the fictional Jamie's real-life relatives fell. "I hope you appreciate my use of weather-a-tronics to recreate the conditions of the actual day," Allison quips as we arrive at the battlefield and the group looks out across the bleak landscape. "Of course, in Jamie and Claire's day, the land would have been much boggier and the men would have stood knee-deep in blood …"

Outlander is a literary and televisual sensation. Twenty million copies of Gabaldon's eight Jamie and Claire books - from Outlander to Written In My Own Heart's Blood - have been sold across the world. The TV series attracted five million views in the first week alone and a second season has been commissioned. Meanwhile, the fact no British TV deal has been struck almost provoked another uprising as rumours spread it was being delayed by the independence referendum (in case its rebel spirit roused Scots to a Yes vote). When it is aired here - given the clamour, nobody doubts it will be - hundreds of thousands more fans are likely to be won over by its charms.

The Outlander phenomenon, though, can't be measured in numbers alone. Its power lies as much in the passion of its fans as their prolificity. Reading (or watching) it is not merely a hobby; it is a religion. Those who are seduced by the characters proselytise to family and friends. They join online communities such as Outlandish UK where they discuss plot-lines and swap gossip. Recently, their discussions have revolved around the TV series. Q) Which property doubles for Lallybroch? A) Midhope Castle near South Queensferry. Q) Is actor Sam Heughan hunky enough to play Jamie? A) Despite early reservations, everyone seems to love him. Q) And when, oh when, will Scottish people get to see it? A) Most of them have already downloaded it from the internet, if the nervous laugh which travelled round the room at Gabaldon's Edinburgh Book Festival appearance is anything to go by. The fans love the landscape, they love the characters and, let's be frank, they love the sex and violence. "Can you imagine? Rape and murder and pillage, the wars. And love and sadness, of course. It's got everything," sighs 74-year-old Margaret Leonard at the Edinburgh event.

With this global interest, it is little wonder VisitScotland is hoping Outlander will do for Scotland what Game Of Thrones has done for Northern Ireland. HBO's fantasy series has brought an estimated £110 million to the Ulster economy and boosted the number of tourists to 1.8m a year.

In an attempt to replicate that success, VisitScotland has set up an Outlander page on its website and a map which charts most of the film locations. And the signs so far are positive. There have already been several big Outlander events; more than 100 fans from all over the world turned up to a convention in Edinburgh in May (with a second in the pipeline) and Gabaldon visited Inverness and Wigtown as well as the capital, causing a mini-frenzy at every venue. There are companies making Outlander-themed jewellery and many tours on offer. Those which have been going longer focus on the books and sites around Inverness, others on the Central Belt locations used in the TV series, such as Doune Castle, Preston Mill and Culross.

Allison has been running one-day trips for several years, but, after the TV series was announced, he trained new guides to cope with the anticipated spike in demand and devised two, three and four-day tours for those who want to travel further afield. Today's trip is a one-day event. The six people who have signed up are Michael and Nikki DeSarno from Vermont, Adam and Abbey Moehn from Iowa, and Alan and Susan Eastham, from Preston, with the women the instigators and the men tagging biddably along.

Nikki was introduced to Outlander by colleagues 15 years ago and has read the whole series several times; Abbey loves history and chose Scotland over Mexico as a holiday destination because she wanted to experience the Outlander magic for herself. And Susan, like many fans, is bound to the books by emotional ties. They were recommended to her while visiting her son and daughter-in-law in Texas. She bought two copies of Outlander - one for her and one for her daughter-in-law - and they read it, and then the sequels, in tandem on opposite sides of the Atlantic, discussing the twists and turns online.

Today, after Clava and Culloden, the group will visit The Storehouse at Foulis, a building once used to store grain paid as rent until it could be sold; a whisky distillery (bit of a tenuous Outlander link, but everyone seems up for a dram); the Ord House Hotel; and Beauly Priory, where many Frasers are buried. Along the way, they will see a water mill, catch a fleeting glimpse of Castle Leod, hear the myth of the kelpie at Loch Garve and be told many stories about what Gabaldon said or did on her visits to Scotland. As they get to know each other, the women will chat animatedly about the quality of the casting. "Oh, I think Caitriona [Balfe, who plays Claire] is too English and too thin," they will say, as the men stare at their hands. But for the moment they are at Culloden and - as the wind moves across the heather and sedges heavy with droplets - it is genuinely moving. "You get a real sense of what it must have been like for the clansmen," Nikki says. "Now, when I read the books again, I will be able to picture the scene."

Three days earlier and the DeSarnos are among the excited throng which has turned up to see Gabaldon at the Edinburgh Book Festival. Though Nikki's affection for Outlander is enduring, it pales beside that of many of those in the queue which winds its way round Charlotte Square. Near the front are three generations of the same family: Christine Townsley, her daughter Angela Stewart and her grand-daughter Madison, five, all sporting "pocket Jamies" - cut-outs of a kilted Heughan worn as badges. Angela explains she got hooked on the books while on maternity leave waiting for Madison to be born. Desperate for someone to share her addiction, she pushed them on her mother, who was equally taken. Though Madison was exposed in utero, she is clearly too young to have read the books, so how did they persuade her to come along? "We told her Diana is important, like the queen," Angela says. No sooner are the words out of her mouth than Gabaldon appears in a flowing silk brocade top, black trousers and sparkly shoes. Trailing an entourage behind her, she walks to the centre of the grass square and sits serenely in a waiting chair as BBC arts correspondent Pauline McLean fires questions at her.

Later, while waiting in another queue to have her book signed, Angela laughs about the day she lost her dignity after rushing to Doune Castle in the hopes of watching the filming. "When we arrived they were just setting up," she says. "We were told we could wander around so long as we didn't cross the yellow tape, but I snuck past when nobody was looking and fell down the hill on to my bum."

This is another strange trend Outlander has spawned: the guerilla set raider. Fans scour the internet for clues as to where filming might be taking place, rush to the scene and try to outwit the security guards. Leading exponents of this sport include Sam Thomson and Kathryn Campbell Erickson. They arrive in the book festival queue still buzzing with adrenaline from their latest adventure. At an exclusive dinner with Gabaldon for uber-fans the night before, they heard a rumour the crew was at Limekilns, Fife. So first thing in the morning, they headed over. By the time they got there, everyone had gone but trappings of what appeared to be a smugglers' cave had been left behind, so the pair crept in and made merry with the props. In Charlotte Square, they open an iPad to reveal a photo-shoot of their antics: Kathryn creeping up an alleyway with a lantern, Sam rolling a barrel and pretending to eat the artificial bread, and both of them running amok with fake muskets. "Look at us - I'm 42 and she is in her 60s, but that's what Outlander does - it brings out your daft side," Sam says.

Sam, who also runs Edinburgh Tour Guides, became interested in the books when she noticed people on her trips were asking questions relating to Jamie and Claire. Like Allison, she now runs specific Outlander tours, but says she gets asked Outlander-related questions on regular ones too. "I was taking a party up on a day trip to Loch Ness. We weren't anywhere close to it, but a note was passed to the front which read: 'Can you tell us about Culloden?' So I put on the microphone and said two words - 'Jamie Fraser' - and the whole bus erupted."

Evidently, Sam's Outlander obsession has spilled into her personal life; not so long ago she also persuaded her husband to drive her to Culross at 9.30pm because she'd heard they were filming there. "I kept going on about it until he said: 'For God's Sake, get in the car,' and he took me over. They had the stake up ready for the witch-burning."

Back on Allison's tour, we have reached the Ord House Hotel, a white, 17th-century mansion with imposing chimneys which was once the laird's house of the Clan Mackenzie. Having learned Gabaldon once spent the night here and having sneaked a peek at the fireplace in the adjacent room (and agreed that, yes, it does look like the one Jamie lay in front of while wounded), the three couples are now trying to juggle china teacups and tiny pieces of fruit cake as the heads of long-dead stags and foxes look on impassively. Then, from nowhere, Allison produces weaponry - a dirk, a basket-hilted broadsword and a spiked targe. After explaining exactly how each of them would have been used at Culloden, he hands them over to anyone who fancies a go. And this, in essence, is why the tour is successful and why, despite its questionable literary merit, Outlander is such a boon for Scottish tourism. Not only is the series bringing visitors to our shores, but it's also teaching them about our history, landscape and culture. Compared to Braveheart (or Brave for that matter), the books are accurate. Gabaldon prides herself on her meticulous research and she preserves myths which might otherwise fade into obscurity.

As the day comes to an end and Allison drops the DeSarnos off near the station, Alan Eastham gives a wry chuckle and says: "I guess this is the very platform Diana stepped on to when she arrived in Inverness." But it is clear, despite his gentle mocking, he and his fellow travellers have enjoyed themselves. And their experience of Scotland won't end here; the DeSarnos are heading off to Skye, the Moehns to Edinburgh and the Easthams to Dornoch. As for Allison, he has lots more tours to cram in before the end of the season. A few weeks after ours, there is one which sees five countries and four continents represented in his eight-seater vehicle. "There was a woman from California who had never read Outlander at all. As we said goodbye, she told me how eye-opening it was to be with people who had not met before and yet were so enthusiastic about this shared interest. She was going straight out to order the books." Another convert, ready to spread the word. n