Paris is to get its first skyscraper for over 40 years after Herzog & de Meuron won planning permission for its 180-metre-high Tour Triangle.

Plans for the controversial triangular tower were approved by city councillors last night, overturning the decision made by the same committee in November last year to reject the tower.

Anne Hidalgo, the pro-development mayor of Paris, tweeted that she is "proud and happy that Triangle can be born in Paris", adding that the project will create 5,000 jobs during its construction and a further 5,000 jobs once built.

Once built, Tour Triangle will become the city's third tallest building after the 324-metre Eiffel Tower and the 209-metre Montparnasse Tower – the last building over 100 metres to be built in the French capital.

Backed by property giant Unibail-Rodamco, the skyscraper will contain a 120-room hotel, co-working office space and cultural facilities. It is proposed for the Porte de Versailles neighbourhood, in Paris' 15th arrondissement.

Herzog & de Meuron – the Swiss firm known for projects including the Beijing Olympic stadium and New York's Parrish Art Museum – says the building will restore the historical axis formed by the Rue de Vaugirard and Avenue Ernest Renan.

It has been met with fierce criticism by local residents, who claim the building will overshadow them, while some politicians have alleged that the design is unsustainable.

But on Tuesday the project was granted planning permission, with a narrow majority of 87 votes in favour and 74 against, according to local reports.

This second vote took place after Socialist Party mayor Hidalgo, one of the project's biggest supporters, declared the original poll invalid, amid claims that some conservative councillors broke the rules by disclosing how they voted. This time around, it was carried out in private.

Herzog & de Meuron first unveiled the design in 2008. Since then, Parisian planning law has changed to permit construction of residential towers measuring up to 50 metres and office blocks up to 180 metres within the city's arrondissements.

Earlier this year, French architects Hamonic + Masson & Associés and Comte Vollenweider Architectes completed a 50-metre-high housing development in the city – the tallest residential building in Paris since the 1970s.

"The change in regulations is a historic moment," the architects told Dezeen. "Paris is cautiously allowing tall buildings back into the city."

Before that, the height of all new buildings was limited to just 37 metres – a response to the controversy triggered by the construction of Tour Montparnasse, which was completed in 1973.