How do you turn a 100-metre-tall incinerator in the heart of Copenhagen into a social and cultural hub? By building a ski slope on the roof, of course.

The unlikely combination of green energy and alpine sport was the winning bid in a competition to design a new waste-to-energy plant which aims to be one of the cleanest in the world when it opens in 2016. For the winning architect, Bjarke Ingels, it made perfect sense to inject a bit of fun into the proceedings.

"When you spend 3.5bn kroner [£424m] creating an energy plant in the middle of Copenhagen you make sure it doesn't become an ugly box that the neighbours will protest against and clutters the cityscape," he said.

"You have to make sure it becomes a public park, an attraction. And when the kids come to go skiing on top of the plant they will probably be curious to find out what's going on inside the mountain."

Ingels grew up wanting to become a graphic novelist, but the 36-year-old Dane is now hailed as one of the most exciting architects of his generation.

For the 2010 Shanghai Expo he gave visitors a sense of sustainable life in Copenhagen by moving the city's most famous landmark, the Little Mermaid statue, to China, complete with her own pool of water from the city's harbour. Visitors on bikes viewed it from spiralling cycle lanes inside the Danish pavilion.

"I work with the idea of hedonistic sustainability, which is sustainability that improves the quality of life and human enjoyment," said Ingels. "The fact that Copenhagen is so clean you can actually jump in the harbour [water] in the city centre is almost a miracle. The city is sustainable but doesn't become synonymous with making lots of sacrifices.

"People are willing to make sacrifices from time to time but they are not going to stop driving their kids to football. People don't drive cars because they want to pollute; they drive cars because they want to visit their friends. It's not about changing our behaviour – it's about designing our society in a smarter way. For example instead of dumping our waste we start to see it is a resource – one tonne of waste almost equates to two barrels of oil."

The waste-to-energy plant, which will be Copenhagen's tallest building, will replace a 40-year-old incinerator located in an industrial area on the fringes of the city centre. More than 50% of waste in Denmark is already used to create energy and the new power plant will be 20% more effective than its predecessor. The building will be wrapped in a green facade created from planters and a lift inside will guide visitors to the top of the "ski mountain" while offering them views of the machinery inside.

To remind visitors of the city's carbon footprint, the smokestack on top of the plant will eject a 30-metre smoke ring every time a tonne of CO 2 is released.

"One of the problems with emissions is that they are so abstract and intangible," Ingels said. "You can see there is smoke coming out of the chimney but you don't really know whether this is a significant amount. In Copenhagen in 2016 you will simply have to count the smoke rings.

"You are turning a factory into a public park and the chimney, which traditionally is a symbol of the problem, is now becoming something playful."

Ingels's studio, BIG, made its name designing a string of innovative residential buildings in Copenhagen, including the award-winning Mountain Dwellings, where flats were stacked on a multi-storey car park and furnished with individual roof gardens. The firm has won several international commissions in recent years, including an apartment building on Manhattan's west side and a new town hall in the Estonian capital, Tallinn.

For the town hall project, Ingels plans to add a huge mirror to the slanted roof of the tower that houses the city council's meeting hall. He calls this the "democratic periscope".

"When the politicians need to make a tough decision they can look up to the roof, which will work like a giant periscope, reflecting views of the city," he said.

"When citizens gather to protest the periscope will work the other way so they can see whether some of the politicians are absent or if they are asleep – and if people have binoculars they can even read the meeting notes.

"It's a type of radical architectural realisation of political transparency."

• This article was amended on 3 July 2011. In the original 3.5bn kroner was converted to £364m. This has been corrected.