Like one skyline perched on another, the latest mega-building by Rem Koolhaas towers over the starchitect playground of Rotterdam. But why was it even built? Oliver Wainwright gets a guided tour

If you put the last 50 years of architecture in a blender, and spat it out in building-sized chunks across the skyline, you would probably end up with something that looked a bit like Rotterdam. Walking the streets of the Netherlands' second-largest city is like trawling a back catalogue of architects' bold dreams and daring attempts. There are buildings shaped like sharpened pencils and forests of floating cubes, towers dressed in bright red pinstripes and blue harlequin chequers, odd lumps and improbable cantilevers thrusting out in all directions. All this is the consequence of the city suffering a bombardment of two things: bombs and architects. Rotterdam was flattened by the Luftwaffe during the second world war and has since served as a hotbed of experimentation, becoming a natural home for the country's architectural avant garde. Since the construction of Europe's first pedestrian shopping zone here in 1953, an idea imported from the US along with kiosks in the shape of oranges and hot dogs, the city has thrived on promiscuous sampling. It is a jumble of bits and pieces, full of echoes of elsewhere, giving the overall impression of paper-thin surfaces held together in an energetic collage.

Now the country's most celebrated architect, Rem Koolhaas, has just completed the nation's largest building here, and one of the biggest in Europe. It is a gleaming beacon of prosperity, a monument to Rotterdam's rude economic health – built at a time when scores of such office blocks lie vacant across the city.

Given the implausible context, De Rotterdam seems appropriately unreal, a dreamlike stage set of financial capital that takes the city's cut-and-paste urbanism to the next extreme. Filling a hefty chunk of the southern skyline, at 150 metres tall and more than 100 metres wide, De Rotterdam looks like someone has sliced up the drawings and stuck them on the horizon – but not put the pieces back together quite right.

Four simple office blocks rise from an elevated podium, only to be cut in half and shuffled up in the wrong order, like a game of architectural Misfits. The resulting form is of a skyline perched precariously on top of another skyline, each block resting on the shoulder of the next in a staggered huddle. The entire thing is clad in a continuous surface of slender aluminium mullions from top to bottom, which shimmer like silvery corduroy, recalling New York skyscrapers of the 1960s. It could be the twin towers of the World Trade Center, resurrected in a Frankenstein muddle.

Manhattanism brought back to the hometown ... De Rotterdam. Photograph: Ossip Van Duivenbode Photograph: Ossip Van Duivenbode

In the headquarters of Koolhaas's Office for Metropolitan Architecture (now simply OMA), to the north of the city, where armies of bleary-eyed interns are summoning mysterious shapes from blocks of blue Styrofoam, there is a mild panic of public relations staffers. Rem has arrived, and overturned their plans: he wants to drive me to the building himself.

"This is our longest-running project," he says, awkwardly folding his tall frame into the bucket seat of his black BMW sports car, as his assistants scramble into a car behind. "It began in 1997, but it only became possible to build it during the financial crisis – when the contractors were cheap enough to do it."

A literal product of the recession, this sharply tailored corporate leviathan is conceived as a "vertical city", housing not just 70,000 sq m of office space, but 240 apartments in the block to the west, and a 285-room boutique hotel in the block to the east, sitting on a chunky plinth of conference facilities, car parking and restaurants. It is the latest €340m (£285m) part of "Manhattan on the Maas," a vision launched in the early 1990s to transform the Wilhelminapier, a little spit of land on the south bank of the River Maas, into something resembling New York – if you squint a bit.

As we roar through the city centre at ferocious speed, the site comes into view. In among the majestic old brick warehouses of the shipping trade now stands a brash collection of starchitects' castoffs. There is a squarish stone shaft by Alvaro Siza, an irregular stack of coloured blocks by Mecanoo, a glowering grey hulk by Norman Foster and a convoluted assemblage by Renzo Piano, complete with a leaning wall of LEDs. With blocks of childlike simplicity, wrapped in a sleek skin of delicate ribs, Koolhaas's offering rises above the surrounding din with cool authority. He may be last to the party, but this contribution is bigger and more sophisticated than them all.

"The most important thing about this project is your perception of its size and mass as you drive over the bridge," says Koolhaas, hunched over the wheel, his frail voice barely audible above the roar of the engine, as we begin our ascent of the boomerang-shaped road of the Erasmus Bridge. "We calculated how the view would change as you approach along this curving path."

When you first see it on the horizon, the building seems scale-less. It could be a miniature model or a massive mountain, the blocks slipping and sliding past each other with no recognisable sense of proportion. It looks utterly surreal, glimmering like a mirage in the low winter sun.

It is an effect Koolhaas has been pondering since 1979, when he designed an unrealised scheme for the other side of the river, predicated on the same idea of a wall of shuffling blocks. "Any structure will be noted in passing, at bewilderingly different speeds and angles," he wrote of the riverside Boompjes site, a few hundred metres to the northeast. By slicing the blocks up, he continued, "the slits between the towers … deliver more than openness; the experience of passing the slab shows stroboscopic flashes of the city". With characteristic certainty, he concluded that this effect created "an accordion movement that made the composition of 'towerslab' infinitely dynamic".

More than 30 years later, and after 16 years of development (De Rotterdam began in 1997, but has stopped and started ever since), Koolhaas's dynamic "towerslab" has now been realised. But is it anything more than an optical trick, a game of dancing facades best viewed from a distance? "That's all you need to see. The rest is just a cheap office building," he says, before leaving me to explore the interior for myself.

'Vertical living' ... De Rotterdam. Photograph: Ossip Van Duivenbode Photograph: Ossip Van Duivenbode

Like other recent mega-projects by OMA, such as the Shenzhen Stock Exchange, most effort has gone into composing a beguiling envelope, leaving the interior to prosaic commercial realities. There are some attempts within the gargantuan floors to choreograph moments of drama and intrigue. You enter into a lofty lobby space, where banks of escalators rise through a seven-storey atrium, past glazed walls of car parking – a grittiness that jars nicely with the world of silver marble below.

In places, the effect of having chunks of the building stick out up to eight metres makes itself felt: vast concrete trusses march across the floor, forming great structural V's and W's. Earlier designs made a bigger show of this zig-zag construction on the facade, but cost-cutting reduced structure to the essential, rather than theatrical.

The apartments – which will be some of the most expensive in the city – offer spectacular views, but as you might imagine, they feel a little like living in an office, staring out through those densely spaced mullions. The novelty of "vertical city" living, where you get out of bed only six metres away from someone at a desk, might wear off fairly quickly, too.

Frankenstein muddle ... De Rotterdam. Photograph: Ossip Van Duivenbode Photograph: Ossip Van Duivenbode

It is too early to tell how this Goliath will function when its floors have been filled, but there remains a strong sense of uncertainty as to who or what will occupy this ample acreage. A speculative building initiated by a private developer, it only went ahead when the municipal government agreed to rent a substantial chunk of the office space. In doing so, it will vacate two other towers to the west of the city, designed by SOM in the 70s, which it rescued in the same way when the real estate market crashed in 1976. As history repeats itself, so continues the vicious cycle of speculation, developers cheered on and bailed out by the government, thirsty for the next iconic project that will bring the magic fairy-dust of inward investment. Or will it?

"The building is a cynical and brutal monument to the city's delusions of grandeur," says Wouter Vanstiphout, professor of design and politics at Delft university. "While Amsterdam is trying to fill its empty offices, Rotterdam is building more and more, but there's no one to go in them. It is madness when there is 30% vacancy across the city – it follows the same logic as saying, 'Let's build houses, because we need more people.'"

I put this to Koolhaas, but he shrugs it off. "It's the same across Europe," he says, batting away the idea that he might be fuelling the city's vanity. "Buildings aren't empty for ever, and we've designed this to accommodate any amount of change."

For him, De Rotterdam is the culmination of a more personal story. It represents the realisation of a decades-long fixation with the thrilling hyper-density of "Manhattanism", first cultivated in his student manifesto, Delirious New York. At the age of 68, he has finally brought back a contorted slice of that city's vertiginous madness to his home town. There is a sense of nostalgia in his voice as he drops me on the street corner, before driving off to his next appointment. "The weird thing is that this building might look cold or harsh, but we get grandmothers now writing to us saying they like it. Which has never happened before."