The machine, featured in Robert Harris's best-selling novel about British attempts to crack the code, went to a Cheltenham-based dealer at Christie's in South Kensington, London.
Winston Churchill, Britain's wartime prime minister, relied heavily on the work of the cryptologists at the intelligence headquarters at Bletchley Park, Buckinghamshire.
The Germans never realised their complex ciphers had been cracked, and this gave the Allies a vital advantage as the war progressed.
The Enigma device fits into a wooden case slightly smaller than a briefcase. A keyboard was used to type in the message, then three wheels encrypted the message according to a key combination. The corresponding letter then flashed on to another keyboard.
Perhaps the most significant use of Enigma was in directing German U- boats in the north Atlantic, where Britain relied heavily on the safe passage of supplies from her north American allies.
Christopher Proudfoot, an expert in the field who auctioned the Enigma machine, said: "There are not many left in existence."
Commenting on the price of this machine, which was brought in from France, he said: "It was towards the lower end of the range we expected, perhaps because its wooden case has been refurbished.Reuse content