Russian Prime Minister Vladimir Putin announced the deal on Tuesday following intergovernmental talks with Hungary. The project falls within the framework of the South Stream project to pump gas from Russia to Europe via the Balkans.
"A separate document on building a large underground gas storage facility on the territory of Hungary has been drafted. Hungarian company MOL is Gazprom's partner in this project," Putin said.
"The gas storage facility will have a capacity of over 1 billion cubic meters. This is a large volume, which will enable us to ensure energy security, and the stability of the Hungarian energy sector," he said.
Gazprom said a final decision on investment in the construction of the storage facility would be made by the end of 2009.
The facility would be put into service in 2012-2013.
The South Stream pipeline is designed to pump 31 billion cubic meters per year of Central Asian and Russian gas to the Balkans and on to other European countries, but its capacity could be increased by a further 16 billion cu m. The project involves Bulgaria, Serbia, Hungary, Italy and Greece.