When the young Danish architect Jørn Utzon won the international design competition for the Sydney Opera House in 1958, his plans were holistic, comprising not just the unlikely structure of the building but the art within it, too.

Utzon wanted to hang the walls with modern art that would complement the sculptural effect of his architecture – names such as Picasso, Matisse and Charles-Édouard Jeanneret-Gris, the pioneering modern architect and artist known by his pseudonym, Le Corbusier.

Picasso and Matisse haven’t yet made it to Bennelong Point, where the Opera House sits, but on Tuesday morning – 57 tumultuous years after Utzon commissioned the work, and a year after it was sold to the Opera House at auction for more than A$400,000 – a 6.5-square-metre wool tapestry by Le Corbusier was finally unveiled in its intended home.

“Tapestries tell stories, and few more than Les Dés Sont Jetés (The Dice Are Cast),” the Sydney Opera House chief executive, Louise Herron, told the small crowd of donors and media gathered at the launch. Stories need a hero, and Utzon made an audacious one: back in 1958, Le Corbusier was at the height of his career and fame, and famously unwilling to collaborate. Barely starting out in the industry, Utzon had no reason to expect his support – but that didn’t stop him from asking.

He wrote to his idol, boldly sending his designs of the Opera House and asking Le Corbusier to contribute in the form of “decoration, carpets and paintings”. His idol wrote back, and by October 1960 the young Utzon was the proud owner of a striking tapestry, signed – very prominently – by Le Corbusier.