"There is a museum of the Shoah in all of Europe's major capitals and it seemed obligatory to me for there to be one in our country, too," Culture Minister Gennaro Sangiuliano said.
The museum is likely to be located across from the Villa Torlonia, a site of symbolic importance that is home to 3rd and 4th-century Jewish catacombs.
It is also the former residence of Fascist dictator Benito Mussolini, who rented the property for one lira per year.
"The Rome city administration will do its bit so that the work is done as fast as possible," Mayor Roberto Gualtieri said.
Luca Zevi, the architect behind the project, said work should start by the end of spring.
ANSA