The quango hopes that the York bunker, built in 1961, will become a popular visitor attraction.
The bizarre structure, which was built in the year before the Cuban Missile Crisis, was one of 29 headquarters buildings dotted across the UK that formed part of the United Kingdom Warning and Monitoring Organisation.
The bunker was eventually decommissioned in 1991 with the signing of a non-aggression treaty between NATO and the Warsaw Pact countries.
EH property development director Tim Reeve said he was excited by the addition of the bunker to the portfolio.
'We are delighted that we have been able to open up this fascinating and unique structure, an outstanding example of its type, to the public and display its exceptional artefacts and collections,' he said.