Designed by Austrian architect Margaret Schutte-Lihotzky, the kitchen started life in about 1925 on a housing estate in Frankfurt, Germany, and has been in use ever since.
According to the museum, the groundbreaking design became the prototype for all fitted kitchens and its labour-saving layout 'fulfilled the Modernist ideal of making life more efficient'.
Among the revolutionary features is an ironing board hinged to the wall, a built-in rubbish bin emptied from a door in the adjacent hall and a moveable ceiling lamp mounted on a rail.
However, because fridges were rare at the time, cool storage was provided by a floor-level cupboard vented from the outside.
The kitchen became an instant hit around the world and in 1929 even became a movie star. This film, on how the kitchen worked, will be shown as part of the exhibition, which runs from April 6 to July 23 next year.
Speaking about the exhibition, V&A curator Christopher Wilk said: 'Our world today was fundamentally changed by Modernism.
'It was the key point of reference for art, design and architecture in the 20th century. It was that big and that important.'