The set of seven hardbacks published by Bloomsbury went on sale in one lot at Cameo Fine Art Auctioneers in Berkshire.
A spokesman at the auction house said the £17,800 figure is the "hammer price" and does not include buyer's premium, which is an extra 15% plus VAT.
Each illustrated cover has been signed by the author JK Rowling without a dedication.
The Harry Potter series included The Philosopher's Stone, The Chamber Of Secrets, The Prisoner Of Azkaban, The Goblet Of Fire, The Order Of The Phoenix, The Half-Blood Prince and The Deathly Hallows.
The estimated sale price was £15,000 to £20,000.
Earlier this month, an avid Harry Potter fan paid £25,000 for an 800-word prequel to the series, penned to raise funds for charities English PEN, which works to promote literature, and Dyslexia Action.
In January this year, Rowling donated a set of seven signed titles to raise cash for Portobello Rugby Club in Edinburgh after it burned down. The sale raised £6,960.
And in December last year, a new Rowling work, The Tales Of Beedle The Bard, fetched £1.95 million at auction.
Amazon bought the book, which was hand-written and illustrated by the author.
Only seven copies exist: six were given to Rowling's close friends and the seventh was auctioned to raise money for her charity, Children's Voice.
