An outpost of the V&A museum in London, the £80 million V&A Dundee is Scotland's first design museum. Located on the on the banks of the River Tay, it opens to the public on 15 September.
Kuma designed the building to evoke the dramatic cliffs of Scotland's coastline.
"The big idea for V&A Dundee was bringing together nature and architecture, to create a new living room for the city," he said.
"I'm truly in love with the Scottish landscape and nature," he added. "I was inspired by the cliffs of northeastern Scotland – it's as if the earth and water had a long conversation and finally created this stunning shape."
Built on reclaimed land, the museum stands at the centre of a £1 billion transformation of Dundee's former docks.
Kuma said he hopes the building, which is his first in the UK, will bring people from all around the world to Dundee.
"I hope the museum can change the city and become its centre of gravity," he said.
The building is formed of two angular volumes.
These are clad in 2,500 horizontal concrete panels, which connect on the first floor to form a single building.
The museum extends over the River Tay with a pointed corner that protrudes like the bow of a boat. This prow-shaped space contains the museum's large entrance space, cafe and shop, with timber walls the reference the building's concrete exterior cladding.
V&A Dundee's galleries, which showcase items demonstrating the importance of design and Scotland's design achievements, are accessed by a ceremonial staircase in the foyer.
On the first floor, the museum's 1,100 square metre temporary gallery, and the permanent Scottish Design Galleries, are accessed from a central foyer.
The Scottish Design Galleries display 300 items that showcase designs from across the country, taken from the V&A's collections as well as pieces from private collections.
The centrepiece of the Scottish Design Galleries is the rebuilt interior of Charles Rennie Mackintosh's Ingram Street Tearooms.
The interior of the Oak Room, which has been in storage since 1971 when the building was demolished, has been restored and reconstructed through a partnership between V&A Dundee, Glasgow Museums and Dundee City Council.
"It is also fitting that the restored Oak Room by Charles Rennie Mackintosh is at the heart of this building as I have greatly admired his designs since I was a student," said Kuma.
"In the Oak Room, people will feel his sensibility and respect for nature, and hopefully connect it with our design for V&A Dundee."
A terrace, accessed from the Scottish galleries and from the foyer, will give views across the River Tay. A restaurant overlooking the entrance hall, auditorium and leaning spaces are also located on the first floor.
The museum's opening temporary exhibition is called Ocean Liners: Speed and Style. It is organised by the V&A and the Peabody Essex Museum in Salem, Massachusetts.
Kengo Kuma won the competition to design the outpost for the V&A in 2010, beating a shortlist including REX, Sutherland Hussey Architects, Steven Holl Architects, Snøhetta and Delugan Meissl Associated Architects.
V&A Dundee is the London museum's first permanent outpost outside the city – although it also recently collaborated on the Design Society museum in Shenzhen.
It follows the trend of some of the world's largest cultural institutions to expand from their original premises.
The Louvre recently opened a new museum in Abu Dhabi designed by Jean Nouvel, Pompidou has opened a gallery in Metz designed by Shigeru Ban and Jean de Gastines, while the Guggenheim has proposed establishing galleries in Helsinki, Vilnius and Abu Dhabi.
"After years of planning, we are thrilled at being able to celebrate the realisation of the first V&A museum in the world outside London," said Philip Long, director of V&A Dundee.
"This cultural milestone for the city of Dundee is also a landmark moment in V&A history – we're extremely proud to share in this exceptional partnership, the first of its kind in the UK, and to have helped establish a new international centre for design that celebrates Scotland’s cultural heritage," added Tristram Hunt, director of the V&A.
Photography is by Hufton + Crow.