The central focus of the painting is a giant mechanical elephant. It is round and has a trunk-like hose protruding from it. The figure's round body was modeled after a photograph in an anthropological journal of a clay corn bin from a southern Sudanese tribe, the Konkombwa. Celebes suggests "ritual and totemic sculpture of African origin", evidenced by the totem-like pole at right and the figure's bull horns. The painting uniquely combines found imagery and tribal elements.Ernst's creature has a frilly metallic cuff or collar, and a horned head and tail. The low horizon emphasizes the creature's bulk, and the gesture of the headless mannequin introduces the viewer to the figure. The mannequin wears a surgical glove, a common Surrealist symbol. This nude figure may have a mythological connotation, suggesting the abduction of Europa by Zeus while disguised as a bull.
Ernst painted The Elephant Celebes in Cologne in 1921. The French poet and Surrealist Paul Éluard visited Ernst that year and purchased the painting and took it back to Paris. Eluard would buy other of Ernst's paintings, and Ernst painted murals for Eluard's house in Eaubonne. It remained in Eluard's collection until 1938 and was then purchased by the English artist Roland Penrose. It has been in the collection of the Tate Gallery, London since 1975 and is displayed in the Tate Modern. The back of the canvas is decorated with some doodles that are seemingly unconnected to the subject matter on the front of the canvas, including two figures holding golf clubs adjacent to the word "GOLF".