The exterior of the Zeitz Museum of Contemporary African Art in Cape Town

Twinkling like rows of cut-glass decanters in a well-stocked drinks cabinet, the faceted windows atop Cape Town’s new contemporary art museum rise as a crystal beacon above a motley jumble of wharves, warehouses and shopping malls.

The windows shine out from the crown of a majestic concrete grain silo that has stood here since the 1920s, once the tallest building in sub-Saharan Africa, now reborn as the continent’s answer to Tate Modern, which opens next week.

“We could have so easily knocked it down and built a big shiny spaceship of a museum instead,” says Thomas Heatherwick, the British designer of the R500m (£28m) Zeitz Museum of Contemporary African Art (Mocaa), the first such institution of its kind in Africa.

“But the danger would have been that people would just come to take a selfie and not go inside. In a place that doesn’t have a strong museum-going culture, our challenge was to make compelling innards, to lure people in to see the art.”

The building’s guts certainly have the jaw-dropping, selfie-friendly wow factor he was hoping for. In one of his most audacious party tricks to date, Heatherwick has excavated a gigantic ovoid atrium from the centre of the silos, revealing a thrilling space of concrete cylinders that plunge from the ceiling like carved stalactites, through which stairs spiral and glass elevators glide. It is a spectacular act of architectural mutilation that makes Gordon Matta-Clark’s penchant for cutting holes in houses look like mere tinkering.

Such a gravity-defying feat wasn’t easy – in fact, it wasn’t initially possible. The rickety 1920s concrete tubes, at just 180mm thick, weren’t capable of being chopped up so brutally, so a new 250mm sleeve of concrete had to be cast inside each of the cylinders. The building was essentially made anew before it could be sliced up in a Herculean ballet of jackhammers, diamond rope and double-bladed circular saws.

The museum’s atrium at night
 The museum’s atrium at night. Photograph: Iwan Baan

The result, however artificial it may be, is nonetheless a powerful piece of constructed archaeology, the aggregate of the new cylinders contrasting with the old, their edges polished like nougat, while the atrium void plunges through the floor to reveal the basement where conveyor belts once shuttled the grain. How well it performs its role as a space for “monumental interventions”, like the Tate’s Turbine Hall, remains to be seen. For now, Nicholas Hlobo’s dangling creature made of rubber inner-tubes and ribbons gets a bit lost in the soaring geometry.

The next hurdle was how to make the galleries. As Heatherwick admits, “tubes are quite rubbish spaces for showing art,” so two-thirds of the silos have been swept away to make space for conventional white cube galleries, “dropped in like shoeboxes” either side of the dazzling atrium. The resulting spaces are indeed rather utilitarian affairs. The character of the industrial hulk has been banished in favour of white plasterboard walls and suspended grey resin floors, which bounce underfoot with an uneasy cheapness. Thankfully the basement level has been left as a raw, as-found space for installations, but more of the rugged spirit would have been welcome throughout.

If it feels like an amazing atrium with an OK gallery attached, the project’s unusual gestation explains why. What to do with the ageing silo had long vexed the V&A Waterfront, the company in charge of the 123 hectares of former docklands, which has been developed piecemeal since the 1990s as an odd mishmash of retail, office and seaside attractions.

“The silo was our cathedral,” says the company’s development director Mark Noble, “but we had no idea what to put in it.”

The museum (near bottom right) and harbour