The anonymous gift of an artistic masterpiece will provide essential funding for the development of a centre devoted to the causes and cure of human obesity.

The painting is Pablo Picasso's Jeune fille endormie (1935), a portrait of Marie-Therese Walter. The 45-year-old artist spotted the 17-year-old as she emerged from the Paris Metro in 19, grabbed her arm and said: "I'm Picasso! You and I are going to do great things together." She went on to become one of his most celebrated muses.

About 18 months ago, an American approached the University of Sydney with an offer to give it the Picasso, along with jewellery, stocks, money and other paintings. The only conditions were that he remain anonymous, that the painting be sold to support scientific research, and that the university find a way to honour someone special to him.

The donor brought the painting to Australia in person. Given the prohibitive costs of insurance, it was then hidden away in a place known only to the vice-chancellor, Michael Spence, and one other person, while its provenance and authenticity were checked.

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It will now go under the hammer at Christie's in London on 21 June and is expected to make between ?9 million and ?12 million.

The timing means that even this may prove a conservative estimate. Many of Picasso's pictures of women are full of savagery and disgust, but Jeune fille endormie reflects the blissful Thursdays and weekends that he spent with Walter and later their daughter Maya in a secluded country house, the Chateau de Boisgeloup. Dr Spence described the painting as "very vibrant, very happy and extremely accessible".

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Such accessibility has made portraits from this period of Picasso's work particularly popular. Eighty are currently on display at the Gagosian Gallery in New York, and another, Nude, Green Leaves and Bust (1932), was sold last month by Christie's for $106.5 million (?65.5 million) - the highest price ever paid at auction for a work of art.

Whatever the outcome next week, the proceeds will go towards Sydney's Centre for Obesity, Diabetes and Cardiovascular Disease. Work on the centre is well under way, with the ground broken on a A$400 million (?260 million) building, due to open in 2013.

Yet a significant injection of money should still prove "transformative", said Dr Spence, because it will provide a store of "unallocated cash for the incoming academic director to make the appointments that can forge the work of the centre".

"It means that, right from the beginning, you can have people of the calibre and from the disciplines you need - it gives you an opportunity to shape a field."

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Just how transformative it will prove now depends on Picasso.

matthew.reisz@tsleducation.com.