The museum says the 206-million-franc project will significantly expand its space for displaying contemporary art while making it the most important European centre for French painting and impressionism outside Paris.
Referendum results announced on Sunday showed 53.9 percent of voters backing the expansion.
With citizen approval, the city is contributing 88 million francs for the expansion, a sum to be matched by the Zurich art association (Zürcher Kunstgesellschaft), which operates the museum.
An additional 30 million francs will come from lottery funds.
The city has also agreed to take over annual operating and maintenance costs of 17.6 million francs.
The new building, designed by Britain’s David Chipperfield Architects, will be located on the opposite side of a square, the Heimplatz, from the original Kunsthaus Zurich, which was built between 1904 and 1910.
A passageway will run beneath the square to link the Kuntshaus to the new extension.
Chipperfield Architect was appointed to design the building in 2008 after an international competition.
The museum expects that when the new extension opens in 2017 the number of annual visitors will rise to around 400,000 a year.
“Improvements will include the scope for larger-scale presentations in the existing building, with more space for Swiss art, especially Alberto Giacometti,” the museum said in a news release.
“Technically innovative exhibition design in the new temporary exhibitions area, the art garden and an electronic media laboratory will combine to make a visit to the Kunsthaus an even more absorbing and interactive experience.”
Museum management noted that the expansion is made possible in part by extensive private funding.
The 88 million being provided by the association through donors amounts to the “largest private contribution ever made to an art museum in Switzerland”.
The museum currently caters to Anglophone visitors by offering an audio guide in English with admission, in addition to ones available in German and French.