The famous code machine was fished out of the sea last month by divers on assignment for the environmental group WWF.
The team was searching for abandoned fishing nets in the Bay of Gelting in northern Germany.
"A colleague swam up and said: there's a net there with an old typewriter in it," Florian Huber, the lead diver, told the dpa news agency.
The team quickly twigged that they had found a historic artifact and alerted the authorities. During the war, Allied forces worked relentlessly to decrypt the codes produced by the Enigma machine, which were changed every day, to gain vital details about German troop movements.
Ulf Ickerodt, head of the state archaeological office in the German state of Schleswig Holstein, said the machine would now be restored by experts at the state's archaeology museum.
Ickerodt said such finds were valuable because the period was "increasingly threatening to disappear from view" as time passes.
Restoration expected to take about a year
The restoration, which will include a thorough desalination process after so long on the Baltic seabed, is expected to take about a year. After that, the Enigma machine will go on display at the museum.
It is believed that the machine was thrown overboard from a German warship in the final days of the war. Experts think it unlikely that the three-rotor Enigma machine came from a submarine because Nazi U-boats used more complex four-rotor devices.
British mathematician Alan Turing, regarded as the father of modern computing, led a team at Britain's Bletchley Park code breaking center, which cracked the cipher system in 1941.
The breakthrough helped the Allies decipher crucial radio messages about German military operations. Historians estimate that it shortened the war by about two years. Only hubris led to the Nazi code being cracked: the insistence on signing some messages with "HH" (Heil Hitler) ultimately provided the weak spot that the code breakers were able to exploit.
The story of Turing and his team was made into a 2014 movie called The Imitation Game, starring Oscar-nominated UK actor Benedict Cumberbatch.