Smith, from Kirkcaldy, published the “first and greatest classic of modern economic thought” in 1776.
The book took the Enlightenment thinker almost ten years to write at his mother’s home in Kirkcaldy and earned him the title “the father of modern economics”.
The rare first edition copy - which originally cost £1 16 shillings - was one of two Smith kept for his own library, the other now being lost.
It went under the hammer at Christie’s Valuable Books and Manuscripts sale in London, estimated at £500,000 to 800,000.
A bidding battle, starting at £380,000, was finally won by an anonymous telephone bidder who paid a hammer price of £750,000, rising to £908,750 including premiums.
A 1776 letter from Smith to his publisher made £137,500.
Eugenio Donadoni, Christie’s Head of Sale, said the auction had presented “a unique opportunity to acquire the author’s own copy of the foundational text of modern economic thought”
He, who studied Glasgow University and Balliol College, Oxford, published his “Inquiry into the Nature and Causes of the Wealth of Nations” at the age of 52.