Due to open in June 2016, the Pierre Lassonde Pavilion is set to increase the 83-year-old museum's exhibition space by 90 per cent.
The 14,900-square-metre building is designed as a contemporary gateway to the museum's existing campus in the centrally located park, close to the St Lawrence River.
It comprises a trio of glazed blocks with varying opacities, which rise in stepped tiers from the park to the street. A protruding diagonal cuboid will contain a staircase to connect the upper two levels.
"Our design stacked three gallery volumes in a cascade that continues the topography of the park," said Shigematsu. "The activity of the city extends below, providing a new point of interface between the city and the park."
The building will present a transparent facade to Quebec's lively Grande Allée, where a new public plaza will also be created.
The outdoor space will be partially sheltered by the 26.5-metre cantilever of the top tier, which will also sit above a Grand Hall measuring 12.5 metres in height.
A 130-metre subterranean passageway will connect the street to the museum's three existing buildings behind.
Inside the Pierre Lassonde Pavilion, column-free galleries will host installations from the permanent collection and temporary exhibitions. An auditorium, a café and a museum store will also feature.
A "monumental" spiral staircase will rise through the structure, connecting the various volumes and mezzanine levels. The exterior "pop-out" stair will provide visitors with views of the park, the city and the rest of the museum.
On top of each volume, roof terraces will provide space for outdoor displays and activities.
"Art becomes a catalyst that allows the visitor to experience all three core assets – park, city, and museum – at the same time," Shigematsu said.
The Musée National des Beaux-Arts du Quebec aims to preserve and promote both ancient and contemporary Québécois art, as well as showcase international art in the city.
It will inaugurate the new building with five exhibitions showcasing its collections, including a display of Inuit art.
"We are delighted to be only weeks away from welcoming the public into this brilliantly conceived design by OMA, which will do so much to help us celebrate the art and artists of Quebec," said Pierre Lassonde, chair of the museum's board of directors.
"With this beautifully functioning and symbolically important addition, our museum now rises to a new level of service for the people of Quebec City, and a new prominence for visitors from around the world."
OMA New York was established in 2001 as an outpost of the Rotterdam-based firm founded by architect Rem Koolhaas. Its completed projects include the Seattle Central Library, and stores for fashion brand Prada in New York and Los Angeles.
The office is also set to open the Faena Forum cultural centre in Miami Beach this year, and has recently announced its first building in Manhattan.
Photography is by Iwan Baan.