With the release of the second instalment, The Two Towers, this Dane is once again about to show us why he's so great.
When we meet, you would think he had just stepped straight off the set. With stubble creeping across his angular chin, his hair is characteristically unkempt and he's dressed in a suitably rural smock-like shirt. Supping from a strange-looking gold pot of green liquid (a health drink of sorts, it transpires), he keeps the reed-thin pipe to his lips for much of the interview.
There is something other-worldly about Mortensen that makes him so suited to playing the dashing Aragorn who, along with Russell Crowe's toga-hero Maximus in Gladiator, has already entered into cinematic folklore as one of the great screen swordsmen of our time.
Mortensen, however, is reluctant to play up his importance in the ensemble. "I don't think there is one hero in the book," he says. "Every character in the story has moments of weakness and self-doubt, moments of courage and triumph. There are tragic incidents in all our journeys. He is the Ring Bearer; but he is no more the hero than Boromir or Gandalf."
That he was the last to be cast makes his triumph all the more remarkable. Two weeks of shooting had already gone by when Jackson decided his original choice for the role - young Irish star Stuart Townsend - was not right. Viggo was given the call and asked whether he would be prepared to fly to New Zealand the following day for more than a year of intensive filming. Never having read Tolkien's epic saga, it meant forgoing his usual preparation, as well as leaving behind his 14-year-old son Henry, the child from his short-lived marriage to musician Exene Cervenka (from LA punk band X).
"It was a lucky thing," he reflects now, despite the initial dilemma it put him in. "Generally, as far as fate and luck goes, this production with all the changeable weather, obstacles of locations, injury and unavailability, still had something really special coming out of each day, regardless of how bad things looked in the morning. I feel there was a lucky star riding over it, like with Sam in the story, who has this vision of a star over Mordor which is hope for the future no matter how bad it looks."
Fate, indeed, seems to have had a hand in his life, the wheel of fortune finally spinning his way after he was on the receiving end of its fickle finger for so long. At the beginning of his career nearly two decades ago, he was cast in Jonathan Demme's Second World War drama Swing Shift and Woody Allen's The Purple Rose of Cairo, but both times his scenes ended up on the cutting room floor. Since then, his work in films like Carlito's Way, Crimson Tide, Daylight and GI Jane have often been either overlooked, swamped by special effects or stung by bad press.
Meanwhile, his more interesting films for first-time actor-directors Sean Penn (The Indian Runner) and Kevin Spacey (Albino Alligator), as well as for Jane Campion (Portrait Of A Lady) and Gus Van Sant (Psycho), reached only limited audiences. Although he shared top-billing with Sandra Bullock for the rehab drama 28 Days two years back, Mortensen had yet to be given the opportunity to demonstrate his star quality.
"We looked at a lot of people and then we started to look at Viggo's movies," says Jackson. "I believe that fate is often very kind to you. When Viggo came on to the project, fate was being very kind to us. Unlike any other actor I'd ever worked with, he embraced the role of Aragorn so thoroughly. He became that character for 14 months."
Rumour had it that Mortensen lived in the nearby forest for much of his time on-set, wearing Aragorn's torn, mud-stained clothes. Producer Barrie Osborne claims that when Mortensen had his tooth knocked out during a sword-fight, he asked if they could Superglue it back in so they could finish the scene. Mortensen says much of this is exaggerated but admits that he spent his free time fishing and swimming, and being at one with the environment.
"Being in New Zealand was an inspiration, because it is a different place. Creatively, in a lot of ways, it was a bonus. For the story itself, the movie, the intangible things that New Zealand added, in some ways have something to do with the indigenous culture that is alive and well there.
"Some of those forests, mountains or special rivers - there were places you didn't have to be told were sacred places. You'd just be doing some scene, be it an emotional scene or a fight scene, and you felt there was a calmness present.
"It was in tune with the mythological under-pinning of the book."
Blessed with the soul of a poet, Mortensen is an unusual Hollywood star. Born in New York, he led a peripatetic childhood. With his two younger brothers, American mother and Danish father, he moved between Denmark, Argentina and Venezuela before they settled in the USA when Viggo was 11 years old.
He graduated from St Lawrence University in Canton, New York, in 1980 with a degree in Government and Spanish (he's also fluent in Danish and English) and began to act in off-Broadway productions, forever seeking new ways to express himself.
Modest, unassuming and understated, he is an artist in the true sense of the word. He has many off-screen roles - painter, photographer, writer and jazz musician - and has published several CDs of music and poetry, as well as four collections of his art and photographs.
Look carefully at the large murals in the artist's studio in A Perfect Murder; the 1998 thriller in which Mortensen plays a painter who lures Gwyneth Paltrow away from hubbie Michael Douglas, and you can see his handiwork.
Mortensen even has his own publishing company, Perceval Press. He has dedicated his life to making art and it's quite apparent when you meet him.
Softly spoken, and rather humbled by all the attention surrounding him, he is more concerned with the metaphorical meanings of Tolkien's work than with discussing what the films will do for his career.
"The history of the Ring and how tempting that would be is akin to atomic energy and nuclear weapons," he suggests. "People make the mistake of thinking: 'We can harness this and use the atom to make the world safer.' It is inherently evil and appeals to the worst aspects of humanity, in a way.
"In Tolkien's world, and I think in our world too, nothing is, in the beginning, evil - not even Saruman himself. The Ring symbolises what can happen if you aren't careful, if you don't care about your fellow man, hobbit or dwarf. You will lose yourself in this lust for power and control over your environment. Anybody who allows themselves to be tempted by the Ring, thinking that they can control it, really they become diminished by it."
Like Tolkien's Ring, Hollywood may have the power to corrupt, but it's hard to imagine Mortensen succumbing to the shallow charms of celebrity.
Since completing The Lord Of The Rings, he has further cemented his screen image as an action-adventure icon shooting Disney's $50 million Hidalgo. He plays Frank Hopkins, the real-life scout, hunter and cavalry despatch rider who became part of Buffalo Bill's popular Wild West shows. He is bewildered, he says, by the sheer force of interest in him right now. People magazine has already anointed him with an entry on its Fifty Most Beautiful list. Fans now queue round the block at his book-signings. He says if it all disappeared tomorrow he wouldn't care, and you believe him.
What is important, it seems, is his relationship with his son, who briefly appeared in a couple of Mortensen's earlier films. Calling him "an inspiration to me all the time", Mortensen swells with pride. "He has got a great mind and is very perceptive."
Like father, like son.