Authorities said the bodies were discovered in mud and debris during rescue operations in Montecito, northwest of Los Angeles.
"We are saddened to report that this incident so far has resulted in 13 confirmed fatalities, as result of the storm that came through our area last night," Santa Barbara County Sheriff Bill Brown told a news conference, warning that he expected the death toll to increase.
The Santa Barbara County Fire Department said on its Twitter feed it was using dogs to look for victims where multiple homes once stood in Montecito following heavy rain, with more than 20 people reported missing.
The department posted pictures of rivers of waist-high mud flowing through neighborhoods and roads rendered impassable by fallen trees.
"Firefighters successfully rescued a 14-yr-old girl after she was trapped for hours inside a destroyed home in Montecito," it added.
Roads were clogged throughout the region with mudflows shutting down more than 30 miles (50km) of the 101 Freeway and knocking a number of homes from their foundations.
Pounding rain weakened south-facing slopes above Montecito and flooded a creek, sending mud and huge rocks rolling into housing areas.
Emergency services told reporters at least "two dozen" people were missing with "several dozen" homes damaged or destroyed. They said they had rescued scores of residents, including 50 airlifted by hoist.
The highest rainfall total was recorded at five inches (13cm) in Ventura County, according to the National Weather Service Los Angeles.
Much of the affected area is land scorched by the massive Thomas fire last month, where there is no vegetation to soak up the excess water.
About 275 traffic crashes were logged in the California Highway Patrol’s jurisdiction in Los Angeles County during the morning commute -- compared with just 30 reported collisions during the same period on Tuesday last week.
A evacuation order was issued in a section of the Los Angeles suburb of Burbank, which was hit by a mudslide that pulled cars out of driveways and carried them downstream.
The slide also caused a "significant" gas leak, and repair efforts left homes on the street with no gas, electricity or water.
"There were many homes, about 40 to 45 homes, affected by it, a couple homes damaged," Burbank Fire Department Battalion Chief John Owings told local TV news channel KCAL9.
"We performed two physical rescues at approximately 7 o’clock this morning."
At Los Angeles International Airport, flooding forced the closure of the customs area in Terminal 2.
Forecasters warned that while the rain had appeared to subside by late morning, more showers and isolated thunderstorms were expected through the evening, with periods of very heavy rain.
The storm came after a 10-month dry spell in the area following torrential rains in January and February of last year. In 2017, downtown Los Angeles experienced its driest March 1 through December 31 since 1878, with only 0.69 of an inch of rainfall, according to the National Weather Service. Source from Vietnamnews.