Burrell included a provision that it must be housed in a park out with the city, so as not to be affected by air pollution. However, no such site existed until twenty years later, when Glasgow City Council inherited the Pollock Estate. As a result of this, no building existed in which to house the collection. The council ran a competition, eventually won by English architect Gordon Barry Gasson, in collaboration with the first female recipient of the RAIA Award, Australian architect Brit Anderson.

The L-shaped building is home to one of the largest and most eclectic assortments of artefacts and exhibits, with over 8000 pieces ranging from medieval weaponry to Islamic and Chinese art, as well as masterpieces by renowned French artists such as Auguste Rodin, Edgar Degas and Post-Impressionist Paul Cézanne. The collection explores many different facets of creation, from textiles and stain glass windows, back to history to ancient civilisations, with the famous Warwick Vase standing as a centrepiece. The vase, dating back to 2 AD, was unearthed in the ruins of the Emperor Hadrian's Villa at Tivoli.