The Design Museum, which currently occupies a former 1940s banana warehouse in Shad Thames, will relocate to the renovated building, located on Kensington High Street in west London.
John Pawson's conversion of the 1960s building will triple the museum's current exhibition spaces to almost 10,000 square metres, allowing the museum to accommodate the first permanent display of its collection, alongside two temporary exhibitions. It is hoped the move will bring in an extra 400,000 visitors each year.
"We need to do something like what Tate Modern did for contemporary art for design in this country," said museum director Deyan Sudjic at today's press conference at Phillips auction house.
"Before Tate was built there was a sense that contemporary art was somehow at the periphery of things, something that even seems not relevant to the mainstream of British life. It's changed so much. We can do that with design as well."
Pawson's plans for the £83 million transformation of the Grade II* listed building were first unveiled in 2012 and scheduled to complete in 2014.
But the renovation of the building, which has has a distinctive hyperbolic paraboloid roof that dips at its centre, has been "inherently problematic architecturally" and caused its opening to be delayed by two years.
"Museums are special places, the architecture of museums does matter a lot, it's what makes people feel that they've come somewhere special, it's what makes you feel its worth leaving your screen," said Sudjic.
The excavation of a large double-height basement below the building will host galleries and an auditorium.
But the largest of the museum's galleries will be placed at ground level and used for temporary exhibitions.
The museum's first pair of temporary exhibitions will be Fear and Love: Reactions to a Complex World by the museum's chief curator Justin McGuirk and the ninth edition of the museum's Designs of the Year.
A Swarovski-sponsored learning centre and a library funded by the Sackler family will be set on the first floor.
The annual Designers in Residence programme – whose participants will be announced later this spring – will occupy the top floor of the building alongside a restaurant and members' room.
Also located on this floor will be the museum's permanent exhibits, including a Vespa Clubman by Corradino d'Ascani, the Ettore Sottsass- and Perry King-designed Valentine typewriter for Olivetti, and Mikhail Kalashnikov's AK47 assault rifle.
Over 200 popular consumer items will be displayed on a Crowdsourced Wall, with a call for suggestions commencing today on the museum's website.
The spaces will be furnished by Vitra, and a partnership has been set up with publishing house Phaidon to create publications to accompany the exhibitions as well as a book about the museum's history.
The £20-million interior fit-out by Willmott Dixon Interiors is scheduled to begin in June 2016.
Studio Myerscough is designing the permanent display areas, while the museum's visual identity has been overhauled by Fernando Gutiérrez Studio, lighting is being devised by Concord and Cartlidge Levene are creating the signage system.
The museum's current site in Shad Thames will close to the public on 30 June 2016 following its final show, Weekend Punk – a two-day event exploring the legacy of punk design.
The building was sold to Zaha Hadid Architects in 2013 in a deal believed to be worth £10 million. Proceeds of the sale have been gifted back to the museum by designer Terence Conran, who founded it in 1989.
"If you forced me to pick the single most rewarding achievement in my long design career then I would not hesitate to say founding the Design Museum in London," said Conran.
"We are about to move from Shad Thames to new, bigger premises in Kensington, where all our dreams and ambitions to create the best and most important design museum in the world will become a step closer to reality," he added. "It will make my long lifetime in design absolutely worthwhile."
Developers Chelsfield and the Ilchester Estate donated the Commonwealth Institute building and land, together with the cost of refurbishing the shell and core of the building.
Phillips auction house will also hold a fund-raising auction of pieces by leading architects and designers including Norman Foster, Jony Ive, Zaha Hadid and Ron Arad on 28 April.
Renderings are by Alex Morris Visualisation. Photography of the existing building is by Luke Hayes.