The diamond, named 'Lesedi la Rona' was unearthed in Botswana in November.
The rough diamond is 1,109 carats and believed to be more than 2.5 billion years old.
The Mayfair auction, which is the first time a rough diamond of such a size has gone on public sale, takes place at Sotheby's later.
The Lesedi la Rona, which means 'our light' in the Tswana language spoken in Botswana, was discovered by Lucara Diamond Corp's Karowe mine.
"Every aspect of this auction is unprecedented. Not only is the rough superlative in size and quality, but no rough even remotely of this scale has ever been offered before at public auction," he was quoted as saying by the BBC.
According to a study by the Gemological Institute of America, the rough diamond's colour and transparency "exemplify" type IIA diamonds.
Stones in this group are "the most chemically pure and often show extraordinary optical transparency".
Nothing of the size and quality of Lesedi La Rona - which measures measures 6.64 x 5.5 x 4.2cm (2.6 x 2.1 x 1.6in) - has been found in more than 100 years.
The 3,106-carat diamond was cut into nine separate stones, many of which are in the British Crown Jewels, including the Great Star of Africa - currently the largest top-quality polished diamond in existence, the report said.
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