The set includes all seven of JK Rowling's adventures featuring the boy wizard.
The books, which were in a private Scottish collection, include one of only 500 first run copies of the original tale, Harry Potter and the Philosopher's Stone. It is also signed by the author.
They will go under the hammer at Lyon & Turnbull in Edinburgh, the city where Rowling wrote them.
Simon Vickers, Lyon & Turnbull's book specialist, said: "This is a wonderful complete set, but the real value lies in the first book, an extremely rare first edition of Harry Potter and the Philosopher's Stone.
"Only 500 copies were published at first, of which 300 went to libraries and were rebound, and effectively lost. The book became a classic, and the series a publishing phenomenon.
"Later books were printed in their millions. Indeed, Harry Potter and the Deathly Hallows was the fastest selling book in history."