One million visitors a year make their way to Oak Valley, a purpose-built resort that’s a two-hour drive from the centre of Seoul. They come for skiing in the winter and golf in the summer, taking in the mountain scenery and staying in the 1,000 rooms provided by a series of shiny condominiums.

And now they come for the art. Last year, the SAN Museum opened in a monumental building by Tadao Ando that perches on top of a mountain in a landscape of reflective pools. “We carved away the mountain ridge to make the narrow site,” the Japanese architect says. “I wanted to create a garden museum in the sky, a dreamlike museum like no other.” His response when he first visited the spot in 2006, was that it was “the forest of life”. His architectural follow-up is a tight elision of landscape and building.

Ando has form when it comes to art and nature. The Chichu Art Museum he completed on the Japanese island of Naoshima in 2004 – a series of partially buried buildings that snake across the landscape – draws 100,000 visitors a year. Chichu hides itself away as much as the SAN Museum declares its presence. For Lee In-Hee, who went to Naoshima in 2005 when she was contemplating how to house her collection of modern and contemporary Korean art, it was a revelation. “I found it shocking – being underground – and inspiring,” she says. “I decided then to build in Oak Valley and not in the city of Seoul.”

Mrs Lee is a woman of means. She is an adviser to the Hansol Group (a paper and chemicals company that also owns Oak Valley) and the daughter of Samsung’s founding chairman Lee Byung-Chul. “I grew up watching my father collect work by Korean artists, calligraphy and antiques,” she says. “Then in 1970, I happened to visit a gallery and discovered a beautiful contemporary painting of roses by To Sang-Bong. I bought it immediately and concentrated on living artists from then on, works that reflect the identity and history of Korea.”

The new museum, though Hansol’s project, has been named SAN for “Space, art, nature”, and because “san” rather conveniently means mountain in Korean. “We’re not after profit, it’s about creating goodwill,” explains Mrs Lee’s son, Hansol’s chairman, Dong-Kil Cho.

“Healing is a key word in Korean society and we consider a museum where you can enjoy nature and art to be a healing place.”

From May, when it opened, to December last year, the SAN Museum had already attracted 80,000 visitors, with each one paying an entrance fee of anything from Won7,000-Won28,000 (£4-£16), though that won’t put much of a dent in the $70m construction cost.

The SAN Museum has all the traits of an Ando building. Four staggered oblong boxes are linked with triangular and circular courtyards, cool interruptions inside the forceful architecture. “I refer to them as spaces of ‘mu’, literally nothingness or emptiness,” says Ando. “Spaces where people can empty their minds.”

Corridors lined with concrete are fantastically high and long, shadowy and dramatic, almost religious.

But Mrs Lee’s imprint is on this building too. While Ando had originally suggested a black stone cladding, she led him to the more local Paju, a richly honey-coloured stone from an area north of Seoul. She also had the 15-degree angle of the walls off the vertical reduced to five (according to my Korean guides, Japanese fortress walls incline at 15 degrees and, following the country’s annexation by Japan between 1910 and 1945, there are some things Koreans do not care to be reminded of), and she insisted on more glazing – four large windows to Ando’s two.

Park Saeng Kwang’s ‘Wedding Day’

Inside, in dimly lit galleries, displays of ancient paper artefacts include hair ornaments and maps and bottles made of a paper that perfectly mimics animal skin. Then it’s on to the highlights from Mrs Lee’s art collection, itself a lesson in near-history. After 1945, Korean artists determinedly went after a new national art, and here it is: ink-and-wash work with expressionistic brushstrokes, layerings of colour, and a distinctive form of landscape painting. Much of the work here – Lee Hang Sung’s free-form calligraphy, Hwang Kyu Baik’s lyrical surrealism, Han Mook’s spiralling geometric forms, Park Saeng Kwang’s exuberantly bright interpretations of folk tales – will be unfamiliar to western visitors; the exception is Nam June Paik’s flickering screens.

Outside, Ando’s pools are like mirrors, the glassy surface occasionally rippled by a gust of wind. The architect has punctuated the landscape with large-scale works from Mrs Lee’s collection of western sculpture.

A strident red constructivist work by Marco di Suvero sits in a field of red flowers; visitors pass beneath a towering red arch by Alexander Liberman as they head to the building’s entrance. In a separate building are four works by James Turrell, including a skyspace that frames the Korean sky.

As we wander the pale stone paths, in warm sunshine, a polite classical piano soundtrack tinkles out of concealed speakers. “It’s the Glenn Gould CD,” says a SAN employee with enthusiasm. It’s time, perhaps, for Mrs Lee to commission a site-specific soundscape as the last jigsaw piece in this project dedicated to healing and calm. Gould is a considerable artist – but it wouldn’t do much for the atmosphere if Psy got slotted in by mistake.

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