The Persian-engraved stone was owned by the Victorian adventuress and heiress Lady Mary Hood.
It was given to the aristocratic Scot by the Mughal Emperor Akbar II around 1813 during her travels across India.
Passed down through her family, it was made the centrepiece of an Art Deco diamond and platinum brooch around 1925.
The brooch will be sold for the first time at Bonhams London Jewels Sale on Wednesday, when it is estimated to make £40,000 to £60,000.
Lady Hood is now best remembered as the prototype for Ellen in Scott’s famous poem The Lady of the Lake, which was published in 1810. She is also reputed to have been the first British woman to shoot a tiger.
Emily Barber, Bonhams UK jewellery director, said that, due to its provenance and the extraordinary story of its original owner, the brooch had already attracted “significant interest from around the world”.
She added: “This is a splendid jewel with an evocative and impeccable provenance. It has been passed down the female line of the family since Mary Hood’s death and is the first time it has been offered for sale on the open market. It is thought that the emerald was mounted as a brooch by Hennell in around 1925.
“The resulting Art Deco jewel perfectly encapsulates the early 20th century vogue for Indian-inspired jewellery that resonated particularly in England due to Britain’s colonial interests.”
Born in Tarradale, Ross-shire, Mary Elizabeth Frederica Mackenzie was the eldest daughter and heiress of Francis Mackenzie, chief of clan Mackenzie and 1st Baron Seaforth.
Also known as “The Hooded Lassie”, she was used by Scott for his character Ellen Douglas after they became friends.
She travelled to India after marrying Vice Admiral Sir Samuel Hood, who served in the country until his death from malaria in 1814.
Lady Hood is said to have charmed the upper-echelons of Anglo-Indian society, acquiring a taste for smoking the hookah pipe.
The brooch was created in the 1920s by the distinguished British society jeweller Hennell, who set the unique octagonal-cut emerald stone within a frame of black enamel, brilliant and single-cut diamonds and mounted it all in platinum.