Painted during Turner's second visit to Rome in 1828, aged 53, Two Recumbent Nude Figures depicts a reclining woman with auburn hair wearing only a red earring. The beginnings of a second figure in pencil are also visible on the canvas.
Although unfinished, the large-scale oil painting, measuring 5ft by 8ft, appears to show Turner's attempt at portraiture in the style of the old masters.
The image echoes Titian's 1538 portrait, Venus of Urbino, depicting a nude woman reclining on a bed, which hangs in the Uffizi gallery in Florence.
Ian Warrell, a Turner expert and the curator of 18th and 19th century art at Tate Britain, said: "This portrait will stop people in their tracks because it is so completely different to the image of Turner's works that everyone has in their minds.
"We see him primarily as a painter of landscapes, light and atmosphere, and so to see him attempt such an unusual subject, consciously trying to develop that portrait style of Titian and the masters, is a radical departure from the landscapes and shipwrecks with which he is so closely associated."