The work, called Nude, Green Leaves and Bust, was painted in 1932 by Pablo Picasso and is based on his muse, Marie-Therese Walter.
The painting, which was sold in New York last year for $106.5m (£65.5m), will go on display at the Tate Modern in London.
Tate director Nicholas Serota: "This is an outstanding painting by Picasso."
"I am delighted that through the generosity of the lender we are able to bring it to the British public for the first time."
Mr Serota said: "Nude, Green Leaves and Bust is one of the sequence of paintings of Picasso's muse, Marie-Therese Walter, made by the artist at Boisgeloup, Normandy, in the early months of 1932.
"They are widely regarded as amongst his greatest achievements of the inter-war period."
The painting has been borrowed from the unnamed private collector who bought it.
It is not known what security precautions have been taken at the gallery to protect it from thieves and vandals.
A Picasso exhibition will open at Tate Britain next year.
Picasso first met Ms Walter, a model in 1927 and she became his mistress. He began to paint her four years later.
She died in 1977, four years after Picasso.
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