The painting, The Arrival of Spring in Woldgate, is now on display in the centre along with other work by Hockney in a major exhibition of his art which continues until October 23.
It is the first of his works to be owned by the Pompidou Centre and said to be the first to be acquired by a French collection generally. His art sells for such high prices that it would usually be beyond the centre’s budget.
Mr Hockney told FranceInfo: “My paintings are very expensive today, it’s a bit crazy. I gave another large painting to the Tate in London and I think a work of this size is more in its place in an institution.
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“So I’ve decided to part with it – it’s too big for a house and I think this is a very good place for it.”
The 2011 painting depicts woods in the East Riding of Yorkshire. Mr Hockney says the spring in Britain became exciting to him because of having spent many years in California where the hot weather means there is no real spring.
The Pompidou’s Hockney retrospective is in partnership with Tate Britain and New York’s Metropolitan Museum of Art.