The extraordinary works Henri Matisse made during the last period of his life – the large-scale cut-outs on coloured paper, including his famous Blue Nudes – are to be exhibited at Tate Modern next spring.

It will be the most comprehensive exhibition of these late works ever held, with 120 on show, including his Large Composition with Masks from the National Gallery of Art in Washington, Memory of Oceania from the Museum of Modern Art in New York and Tate's own The Snail. These works were displayed together by the artist in his studio, and will be seen together again for the first time during the exhibition.

The artist began to make cut-outs in 1943, according to the curator Nicholas Cullinan, after an operation in his early 70s that left him in ill health and the feeling that he was living on borrowed time. At first the impulse was pure expedience: the works could be made much more quickly than an oil painting. At the same time, "he began to realise the potential in the method, and stopped painting, choosing to focus on the cut-outs," said Cullinan. "He talked about how liberated he felt; how he had been given a second life."

With assistants colouring the paper to precise specifications and then helping to position the works, Matisse would "make cut-outs with a rapid gesture with the scissors, incredibly quickly," said Cullinan. He was also "fastidious and meticulous", redoing and altering the work until it was exactly right.

He became so entrenched in this way of making art that "his work rate accelerated rather than diminished – he would work around the clock and assistants in their 20s remembered being really put through their paces by him. He was still working in 1954, two days before he died."

They were extraordinarily forward-looking works. "They are more like installations or environments than paintings; and they seem very contemporary now. Part of the point of the show is to reconsider them in this light," said Cullinan. "They were a way of collapsing line and colour; at the same time they were a kind of sculpture – carving into pure colour."

Tate Modern's 2014 exhibition lineup will also include shows devoted to two recently departed major figures, Richard Hamilton, the father of British pop art, and the German master Sigmar Polke. There will also be an exhibition devoted to a hugely important figure from the early 20th century, the Russian constructivist Kasimir Malevich.

At Tate Britain, there will be the first big survey of British folk art, an exhibition devoted to Turner's late period, and an exhibition examining the cultural contribution of the critic and scholar Kenneth Clark. The sculptor Phyllida Barlow, known for her works in inexpensive and low grade materials, has been asked to make new work for the Tate Britain Commission, which invites an artist to develop a new work in response to the Tate collection.

At Tate Liverpool a show devoted to Mondrian, marking 70 years since his death, will include a reconstruction of his Paris studio.