It was expected to fetch up to £12,000 in the sale in Edinburgh, but competitive bidding drove it up to double that price and it was bought by an anonymous bidder at the Lyon & Turnbull sale.
In the letter, which is dated January 19 1853, two years before her death, the author thanks pharmacist David Waldie for his praise.
Waldie, from Linlithgow, West Lothian, wrote to Bronte after being impressed by Jane Eyre, published in 1847 under the pseudonym Currer Bell.
Bronte replied in her letter: ''The sincere affection of a reader's gratification is - I scarcely need to say - one of the much acceptable favours in which an author can be repaid for his labours.
''I shall be glad if any future work of mine gives you equal pleasure to that you speak of having found in 'Jane Eyre'.''
Cathy Marsden, book specialist at Lyon & Turnbull, said: "We had huge interest in the letter, particularly from all the press coverage we have had, and it seems to have caught the public's imagination."
Elder sister Charlotte died aged 38 in 1855 while pregnant with her first child.
The sale was part of the Rare Books, Maps & Manuscripts auction, which also included a rare first edition copy of Adam Smith's The Wealth Of Nations valued at £50,000.