The machine, which was constructed in 1943, is one of few that survived the conflict intact, as the German military was given orders to destroy them as it retreated.
The machine includes three rotors and was sold complete with an oak hinged-lid carrying case.
It was sold to an anonymous buyer for 149,000 pounds, significantly more than the expected price of 50,000-70,000 pounds at Sotheby's auction house.
To use Enigma, the operator would type in a message, then scramble it using three, four or five notched rotors, each with 26 possible positions, 'Gizmag' reported.
The German military believed that the encryption granted by Enigma could not be broken, but thanks to Polish cryptographers and the work of codebreakers at Bletchley Park - including mathematicians Gordon Welchman and Alan Turing - the cipher was eventually beaten.