Only 4,760 first editions of Casino Royale were printed, with Fleming’s inscription making this copy particularly desirable.
The book comes in its original heart-covered dust jacket and is being sold by London-based dealer Peter Harrington.
A Peter Harrington spokesman said: “Signed and inscribed copies of Fleming’s first Bond novel are in themselves highly coveted.
“In this instance the association is particularly charming, showing a relationship instrumental in the creation of the character and his legacy.”
Fleming went on to write a total of 14 novels, with more than 100 million copies sold.