A bronze portrait of a woman, made in one of 16 known casts by Edgar Degas and formerly owned by Lucian Freud, has been bought by Leeds Museums and Galleries, having been one of only three works by the artist left to the nation upon Freud’s death two years ago.

Degas’ heirs authorised a series of posthumous bronzes in 1891, fashioned from 72 small figures. He worked on Portrait of a Woman: Head Resting on one Hand privately, and is thought to have shown little interest in being renowned as a sculptor, although 150 wax, clay and plastiline works were found in his studio when he died in 1917.

Curators in Leeds, who will manage the work with the help of the Henry Moore Institute, appear to have benefited from their reputation as the keepers of arguably the finest holdings of 20th century British art outside of London, at Leeds Art Gallery. This is the first Degas piece to enter the collection, joining a particularly hallowed cast of Rodin’s The Age of Bronze, from 1906.

Competition was fierce for the trio of sculptures. Arts Council England awarded them to Leeds, National Museum Wales and National Museums Liverpool’s Walker Art Gallery under the Acceptance in Lieu scheme.

Degas’ best-known sculpture, The Little Fourteen-Year-Old Dancer, caused scandal among his contemporaries when it appeared in Paris in 1881 wearing a real bodice, stockings, shoes, a tulle skirt and a horsehair wig with a satin ribbon.

• Portrait of a Woman: Head Resting on one Hand will be included in a display of the gallery's holdings of French art, brought together in tribute to the Grand Depart of the Tour de France in Yorkshire in summer 2014.

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