Areas east and south of Los Angeles, including San Diego, could see up to an inch of rain.
Further east, parts of Arizona could pick up 2-4 inches of rain, and Phoenix could receive 1.5 inches.
This could trigger flash flooding across the Desert Southwest, with more than 10 million people under flash-flood watches.
The rain will last until Friday, bringing relief to many drought-stricken areas. Much of California is still “abnormally dry,” according to the US drought monitor.
Dry conditions, low humidity and gusty winds will combine to create a heightened risk of wildfires during the next few days.
Later this week the storm system will move East, bringing rain and snow to the Rockies and the Midwest.