Future Library, a public artwork that grows in Nordmarka, Oslo

In the hills above Oslo I'm doing as Norwegians do – wandering through the forest of the Nordmarka. I've been walking for 20 minutes and I've just entered a young stand of spruce trees. The earth is mossy and the trees reach 10 to 15 metres over my head, casting the ground into a salt-and-pepper mix of light and shade. It could be a forest from a fairy tale, but these trees have a very different literary purpose.

What I'm standing among is the construction stage of one of the world's most exciting literary projects: Oslo's Future Library. These 1000 trees, planted here in 2014, will be cut down in 2114 to become an anthology of 100 previously unpublished manuscripts from some of the world's finest authors.

Every year a writer contributes a text that will be held in trust, unpublished, until the year 2114. Already there are works from Margaret Atwood (The Handmaid's Tale), David Mitchell (Cloud Atlas), Turkish writer Elif Shafak and Icelandic author and musician Sjon that will remain unpublished for another 95 years. The texts will be printed on paper made from the trees.

The literary works will be held in trust in a "silent room" in Oslo's new Deichman Bjorvika, a beautiful glass library that's slated to open in 2020 beside the waterfront opera house. The silent room will be lined with wood from the trees that were felled for the planting of the Future Library Forest. Visitors will be able to view the manuscripts, but not read them, until 2114.

Though the Future Library Forest is on Oslo's outskirts, it's simple to reach, with the walk beginning at Frognerseteren. This small village sits at the heart of Oslo's forested Nordmarka – the local name for Oslo's hills and forests – and yet it's still a stop at the end of the city's subway system. The presence of a subway station this far out of the city centre, atop the hills, is testament to Oslo's love for skiing. Sitting high above the city's famous Holmenkollen ski jump (the site of the 1952 Winter Olympics jump events), Frognerseteren is one of Norway's pioneering ski areas and apparently the Norwegian king favours it for his ski trips.

From Frognerseteren station, more than 400 metres above sea level, there are views down to Oslo and the waters of Oslo Fiord. The walk to the Future Library Forest dips past the isolated, chalet-style Frognerseteren restaurant, and sets out across the slopes on a cross-country ski trail that's floodlit in winter. It's a beautiful walk and I share the trail with joggers and cyclists.

The hills are covered in pine trees, but I'm more interested in the forest floor, where blueberries abound, providing snacks as I wander towards this most literate of forests. I will arrive with hands stained purple by berries so thank goodness I won't be handling any books in this growing library.

After about 15 minutes, shortly after crossing a stream, the trail comes to a junction and a wooden sign points up the hill to Fronsvollen. A few steps ahead, another sign points right to Framtidsbiblioteket (Future Library). I have arrived.