This year, Italy has already expelled some 60 Islamist radicals, including four imams, but these are the first expulsions since the November 13 strikes in the French capital.
Interior Minister Angelino Alfano signed the expulsion warrants for the four men, who were known to intelligence services. The video was found at their home.
Italy has ratcheted up its security alert to the highest level possible in the absence of a direct attack on the country after the Paris carnage.
Since Monday, some 2,000 police have been deployed across Rome ahead of the Vatican's Holy Jubilee Year of Mercy which kicks off on December 8 and is expected to attract millions of visitors.