It will be displayed for the first time in The Tomb: Ancient Egyptian Burial exhibition at the National Museum of Scotland on 31 March.
The shroud, which dates to about 9BC, was found during "an in-depth assessment" of Egyptian collections.
A new, permanent ancient Egypt gallery will open in 2018/19.
Dr Margaret Maitland, senior curator of ancient Mediterranean collections, found the folded shroud wrapped in brown parcel paper, with a note written by a past curator in a World War Two service envelope identifying the contents as having come from an ancient Egyptian tomb.
The package had been stored since the mid-1940s.
Conservators gently humidified it so that the fibres became less dry and brittle.
This allowed them to carefully unfold the shroud, a process which took almost 24 hours.
A hieroglyphic inscription on the shroud revealed the identity of the owner to be the previously unknown son of the Roman-era high-official Montsuef and his wife Tanuat.
Dr Maitland said: "To discover an object of this importance in our collections, and in such good condition, is a curator's dream.
"Before we were able to unfold the textile, tantalising glimpses of colourful painted details suggested that it might be a mummy shroud, but none of us could have imagined the remarkable figure that would greet us when we were finally able to unroll it.
"The shroud is a very rare object in superb condition and is executed in a highly-unusual artistic style, suggestive of Roman period Egyptian art, yet still very distinctive."
In ancient Egypt, following mummification a shroud was often wrapped around the body before it was put in a coffin.
In Roman-era Egypt, shrouds became increasingly important as the use of coffins became rarer.
Experts said the full-length, painted linen shroud is unique.
It shows the deceased depicted as the god Osiris.
Curators said because of its owner's direct relationship to Montsuef and Tanuat, whose deaths were recorded in 9BC, it is possible to date the shroud.
The shroud comes from a Roman-era burial in a tomb originally built about 1290BC opposite the great city of Thebes (modern-day Luxor).
First built for a chief of police and his wife, it was looted and reused several times before being sealed in the early 1st Century AD.
It was undisturbed until its excavation in the 19th Century.
The shroud is one of a number of objects from this tomb which are in National Museums Scotland's collections.
The Tomb: Ancient Egyptian Burial, which is sponsored by Shepherd and Wedderburn, will tell the story of this tomb across 1,000 years of use.
According to bbc.com