The council, on the eve of Holocaust Remembrance Day, gave unanimous consent to the project, which had been awaiting approval for years.
The envisioned museum, to be carved out of the grounds of the villa, would include a conference room, library, exhibition room and video-archive.
Mayor Giani Alemanno told ANSA he hopes to invite investors to back the 13-million euro (about $17 million) project "shortly."
The City Council also approved a plaque at the Tiburtina rail station to commemorate Oct. 16, 1943, the day thousands of Jews were deported from Italy.
Fascist dictator Mussolini ruled Italy from 1925 to 1943 and led the country into World War II in 1940 in the Axis with Germany and Japan. In 1938, Mussolini introduced the Manifesto of Race, which stripped Jews of Italian citizenship.