Officials warned those who chose to ignore the orders that they would not have time to get out of the way once a slope gave way, the Los Angeles Times reported.
"Understand this: If there is mud coming down, fire personnel cannot get to you," Steve Martin of the Los Angeles County Fire Department said. "There's a reason for these evacuations."
The risk was increased by recent wildfires that stripped vegetation from the hills. About 1,200 homes were ordered evacuated in the area where a fire in January charred 2,000 acres in the Los Angeles National Forest.
The storm, which began Friday, brought more than an inch of rain to much of Southern California, which has been going through a prolonged drought. By Friday afternoon, about 1.7 inches had fallen in downtown Los Angeles.
The National Weather Service predicted the weekend would bring 3 inches of rain in low-lying areas as the storm moves inland and up to 10 inches in some mountainous areas.
On its Twitter feed, the NWS reported a weak tornado causing no injuries.
Bill Lapenta, a weather environmentalist, told CNN the storm will not do much to relieve California's water shortage. He said much of the water will end up in the sea quickly as it flows down the steep hills.