The 42-storey building, described on Tuesday by Paris Mayor Anne Hildago as a 500-million-euro investment in the French capital, will be the first tower to be built in the city in more than 40 years.
The Swiss architect's design was initially voted down last November, although that decision was annulled by Hildago — who has championed the project — over alleged voting irregularities.
The pyramid, to be built in the 15th arrondissement of Paris, will be the third highest building in the city after the Eiffel Tower (301 metres) and Tour de Montparnasse (210 metres).
It is to house a 120-room four-star hotel, a panoramic restaurant, offices, conference centre and other facilities, including a care home and creche.
Elsewhere in France, Herzog & de Meuron also designed the recently opened 42,000-seat football stadium in Bordeaux, which is to host the European Cup competition next year.
“La Tour Triangle” breaks a long-maintained moratorium on tall buildings in Paris following controversy over the Montparnasse tower, built in 1973 and regarded by many as an eyesore.
A height limit of 37 metres was subsequently placed on buildings, forcing developers to build office towers outside of the city limits.
Despite its height, Herzog & de Meuron's design seduced a majority of Paris councillors for a project to be developed by Unibail-Rodamco, a Paris-based commercial property company.
But the project is controversial, sparking opposition from Greens and residents in the neighbourhood who fear it will destroy the southern skyline of the city.
It's not the first time Herzog & de Meuron have courted controversy.
The firm, founded by Jacques Herzog and Pierre de Meuron, designed the Roche Tower, nearing completion in their home town, as an office building for the pharmaceutical giant.
Admired by some and reviled by others, the 175-metre Roche-Turm is Switzerland's tallest building and dominates Basel's low-level skyline.
The final design for the stepped tower is radically different from a double-helix blueprint initially proposed by the architect firm, ultimately abandoned because of high costs and lack of practicality.
The founders of the firm, both graduates of the Federal Institute of Technology (ETH) in Zurich, have made a name for daring approaches to architecture.
After starting out in 1978, they first rose to prominence with their design to convert the Bankside Power Station in London into the Tate Modern art gallery.
They were awarded the Pritzker Prize, one of the highest distinctions for architecture, in 1978, and were described by The New York Times Magazine in 2006 as “one of the most admired architecture firms in the world”.
The firm now has offices in Hamburg, as well as New York.
The Bordeaux football stadium is just one of several sports stadiums they have designed, including the home ground for the Basel football club, St. Jakob-Park, completed in 2001.
They designed the Allianz Arena stadium in Munich, as well as the Beijing National Stadium, sometimes described as the “Bird's Nest' because of its criss-crossing steel beams, built for the 2008 Summer Olympics.
But apart from monumental buildings, the Basel firm also involves itself in smaller projects.
Its redesigned summit restaurant building at Chäserrugg in the Swiss Alps just opened at the weekend.
The wood structure with a cantilevered terrace welcomes visitors taking the cable car operated by the Toggenburg Bergbahnen to the mountain peak in the canton of Saint Gallen, about an hour's drive from Zurich.
Chäserrugg building houses a restaurant and the terminus for a cable car. Photo: Toggenburg Bergbahnen