Dr Hawley Harvey Crippen was executed in November 1910 after poisoning his wife and hiding her dismembered remains under the cellar floor.
He was caught as he tried to escape to Canada with his mistress, Ethel Le Neve, who was disguised as a boy.
The letters, written while he was in prison and sold in Wiltshire, would remain in the UK, auctioneers said.
Auctioneer Andrew Aldridge described the atmosphere in the saleroom as "frantic" with bidders calling in from Australia and the United States.
He said the letters provided a "fascinating insight" into Dr Crippen's mind during the last few days of his life.
One of his final letters, written to Lady Henry Somerset on 26 October 1910 - less than a month before he was executed - details his relationship with his mistress and his view that "all yet may come right".
Crippen was hanged at Pentonville prison, in London, on 23 November 1910, after an appeal against his sentence failed.
He became the first criminal to be captured with the aid of wireless communication, after the captain of the ship he was escaping on to Canada, the SS Montrose, became suspicious.
The ship's captain sent a telegraph message informing the owners he believed Crippen was on board.
The infamous killer's letters, which are being sold by a private collector, had been expected to make between £3,000 and £5,000 in the sale at Henry Aldridge and Son auctioneers.
Letters written by one of the 20th Century's most notorious murderers have been sold for £11,000 at auction.