The museum near Wakefield, spread out among 200 hectares (500 acres) of parkland, had modest beginnings, founded by Peter Murray in 1977 when he was principal lecturer in art history at Bretton Hall College and had the idea of putting some sculpture in the grounds. Today Murray is executive director of an organisation which is one of the world’s most important open air museums, with 160 staff and 220 volunteers.

Stephen Deuchar, director of the Art Fund and chair of judges, said YSP was “a perfect fusion of art and landscape” that had gone “from modest beginning to one of the finest outdoor museums one might ever imagine”.

Last year was a particularly strong one for YSP with record visitor numbers and a successful exhibition of works by Yinka Shonibare; the restoration of an 18th-century chapel which then had as its first exhibit a new work by Ai Weiwei; and the installation of Roger Hiorns’ Seizure 2008/2013 – a copper sulphate chamber relocated from its initial home, a condemned London bedsit.

Writing in the Guardian last weekend Shonibare said: “For an organisation run on comparatively modest resources, it has produced some of the most exciting exhibitions anywhere in the country.”

Yinka Shonibare’s Frabric-ation exhibition at the Yorkshire Sculpture Park. Photograph: Christopher Thomond for the Guardian

The judges said 2013 was “the culmination of a 40-year journey of steady, strong and visionary leadership that has firmly positioned this outstanding museum as a world leader”.

YSP won from a shortlist that also included Tate Britain, the Hayward Gallery in London, the Mary Rose Museum in Portsmouth, the Sainsbury Centre for Visual Arts in Norwich and the minnow in the field, the Ditchling Museum of Art + Craft, in East Sussex.

The winner was announced by the film and theatre director Sam Mendes at a ceremony at the National Gallery in London. “I’m genuinely honoured to have been asked to be a part of announcing this award,” he said. “The dedication, love, and unbelievable creativity of the six candidates are clear for all to see, as is the creative health of the UK museum community as a whole.

“Financial health is a different matter, however – and in that respect this award is a crucially important boost to one deserving organisation.”

The prize was established in 2003 and known as the Gulbenkian prize for museums and galleries until 2007. The Art Fund took over in 2008 and previous winners include the William Morris Gallery in Walthamstow, north-east London; the Royal Albert Memorial Museum, Exeter; and the British Museum for its History of the World in 100 objects project.

The judging panel this year consisted of Sally Bacon, the director of the Clore Duffield Foundation; the artist Michael Craig-Martin; Wim Pijbes, the director of the Rijksmuseum, Amsterdam; and Anna Somers Cocks, the chief executive of the Art Newspaper.