Brown said at a pre-dawn press conference that the shooting in the town of Isla Vista, near the campus of the University of California at Santa Barbara, "appears to be a mass murder situation."
Police said the gunman was among the dead.
The suspect, driving a black BMW, opened fire on pedestrians from his vehicle at several locations in the town last night, is among those killed.
Police received their first emergency calls about the shooting around 9:30 pm local time yesterday.
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He then crashed into a parked vehicle. When police approached him they "determined that the suspect ... Was dead of an apparent gunshot wound to the head," Brown said.
Police recovered a handgun from the suspect's vehicle.
Authorities believe that the shooter acted alone, and said they are investigating a threatening video posted by the alleged shooter on YouTube as evidence.
Police are "analysing both written and videotaped evidence that suggest this atrocity was a premeditated mass murder," Brown told reporters.
Authorities have not yet released the suspect's name.