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.

Iron ore delivered into China fell 8.3% on Monday after Beijing reported weak export data over the weekend.
China is one of the biggest consumers of the commodity and there are concerns a slowdown in its economy may hurt demand and impact miners' profits.
Shares of BHP Billiton, Rio Tinto and Glencore Xstrata all fell.
Rio Tinto shares ended the day down by 5.7%, while BHP Billiton fell more than 4% on the Australian Securities Exchange.
Fortescue Metals tumbled nearly 10% in Sydney on Monday.
Mining stocks listed in London were also hurt, with Anglo American, Antofagasta and Glencore Xstrata all down by more than 2%.
Recent demand for minerals like iron ore and copper has been driven in part by China's export boom, as well as government-led infrastructure spending.
That has seen miners become increasingly dependent on China for growth.
However, over the weekend, China reported a surprise 18.1% fall in exports for February, compared to the same month last year.
A fall in China's steel futures also hurt mining shares because iron ore is a key ingredient in steel manufacture.
Fears of slowing demand from China have added to slides in other commodity prices, like that of copper, which has dropped to its lowest level in more than seven months.
China is the biggest buyer of the metal, which is used in electronics production and other manufacturing industries.
"Any poor news from China is always going to hit short-term market sentiment, especially in the mining sector, and fears of slower growth will hit base metals," said Steven Mayne, director at IPR Capital.

Princess Road and Princess Parkway in Manchester will be lowered from 40mph to 30mph for an 18-month trial after a proposal was approved by councillors.
There have been two deaths and 84 crashes over the past three years.
A friend of Ian O'Mara, who died when he was hit by a coach on a pelican crossing in 2015, helped set up a petition to change the speed limit.
A coach driver who hit the dog walker in Princess Road was given a suspended sentence after admitting causing death by careless driving.
The change to the speed limit was passed by Manchester City Council on Wednesday, although a date for when it comes into force is yet to be confirmed.
Princess Parkway merges into Princess Road and stretches 3.7 miles (6km).
Campaigner Sam MacWilliam, from Chorlton, said: "The road is very important for people coming into the city, but they need to understand that they are coming off the motorway and into an area where people live.
"There are schools and churches here."
Letters written by one of the 20th Century's most notorious murderers have been sold for £11,000 at auction.
[NEXT_CONCEPT]
Shares in some of the world's biggest mining companies have been hit by a slump in the price of iron ore, amid fears of a slowdown in China's economy.
[NEXT_CONCEPT]
The speed limit on a major route into a city has been reduced following a campaign launched after a man's death.