Firefighters recovered the body of Brunello Canuto, 70, an hour after the incident, La Stampa reported.
A neighbour was also hit by the landslide after the pair left their homes to take a look at the water pouring down a nearby hill, but survived.
The bodies of Carlo Arminese, 73, and his 69-year-old wife, Franca, were found buried in mud in front of their home in the town of Leivi late on Tuesday, Ansa reported.
“The bodies were found close to each other…they were running from their home to try and save themselves,” a firefighter was quoted as saying.
Prosecutor Biagio Mazzeo opened a manslaughter inquiry as the president for the Liguria region, Claudio Burlando, called for "immediate" funding of €150-€200 million to repair damages and implement flood protection measures in a region ravaged by storms over the past month.
The areas worst by the latest floods were the Tigullio Gulf towns of Leivi and Chiavari, where “streets have become rivers” and “hundreds of shops and businesses were flooded”, La Stampa reported.
The storms come after four people died in floods in Genoa and Tuscany in early October.
Ten people in Chiavari were brought to safety in a rubber dinghy on Tuesday night, as torrential rain prompted streams and the River Rupinario to burst their banks.
Two women, one pregnant, were also saved after their home was also hit by a landslide in Leivi.
"We're not playing games," Burlando was quoted in La Stampa as saying.
"Hope needs to be restored in Genoa and Tigullio now. If you don't help businesses and households, they will not recover."