Sheriff Bill Brown said the suspect, confirmed as 22-year-old Elliot Rodger, a student of Santa Barbara City College, was believed to have shot himself in his car after he fought two gun battles with police.
Among the dead were two women, aged 19 and 22, who were gunned down outside a university sorority house and a male student who was shot in a delicatessen.
Police described the spree as "premeditated mass murder".
Rodger's father, film-maker Peter Rodger, was educated in Maidstone, Kent, and was assistant director on 2012 blockbuster The Hunger Games.
The family's lawyer, Alan Shifman, revealed they had called police several weeks ago after being alarmed that he had uploaded several YouTube videos "regarding suicide and the killing of people".
Police interviewed him at his home but found him to be a "perfectly polite, kind and wonderful human", Shifman said.
The shootings began at 9.30pm local time on Friday night (5.30am yesterday British time).
During the rampage Rodger, who had Asperger's syndrome, opened fire at random as he drove around the beach community near the University of California campus.
He shot pedestrians, ran over two cyclists and exchanged gunfire with police officers before crashing his BMW into a parked car. He was found shot dead in the head, believed to be suicide.
Brown said it was a "chaotic, rapidly unfolding and convoluted incident" across 10 separate locations.
Rodger was found with three 9mm semi-automatic guns in his car and more than 400 rounds of unused ammunition, and Brown said he had "no doubt there would have been further loss of life" if police had not intervened.
A further 13 people were injured, including four Rodger ran down and eight who were shot. Seven people remain in hospital, two of whom are in a serious condition.
Rodger had posted several videos online, including one just hours before the attack outlining his plans that Brown described as "particularly chilling".
The sinister recording shows Rodger sat in his car, looking directly at the camera and declaring "the day of retribution" was coming.
In the YouTube video, entitled "Elliot Rodger's retribution", he describes plans to shoot women and promises retribution for his "loneliness and frustration" at never having had a girlfriend.
The student went on: "For the last eight years of my life, ever since I hit puberty, I've been forced to endure an existence of loneliness, rejection and unfulfilled desires all because girls have never been attracted to me."
He complained that he had been at college for more than two and a half years but was still a virgin and had never kissed a girl.
Rodger said: "All you popular kids, you've never accepted me and now you'll pay for it."
He went on: "I'll take great pleasure in slaughtering all of you. You will finally see that I am, in truth, the superior one, the true alpha male."
On his online blog, Rodger wrote that he was born in the UK and moved to the United States when he was five and was attending college in Santa Barbara.
In a post dated April 16, he wrote: "Being lonely in a beautiful place like Santa Barbara is truly a horrible experience.
"As I've said many times, a beautiful environment can be the darkest hell if you have to experience it all alone, especially while having to watch other men walking around with their girlfriends. I wish girls were attracted to me.
I don't know why they aren't."
Police also found a 141-page "manifesto" outlining his plans and talking of how he narrowly missed being found out when police knocked on his door.
Brown said the video was "obviously the work of a madman, adding: "It is very, very apparent that he was severely mentally disturbed".
He continued: "We're analysing both written and videotaped evidence that suggests that this atrocity was a premeditated mass murder."
Brown revealed that the three guns found in Rodger's car - two Sig Sauer P226 hand guns and a Glock 34 Long Slide - were legally bought from licensed firearms dealers and were registered in his name.
Police also discovered more than 40 unused loaded gun magazines in the vehicle, hinting at the extent of his plans.
Brown revealed officers had come into contact on three occasions over the last year, including in January when he performed a citizen's arrest on his room-mate for stealing a candle and last month when Rodger's family asked police to check on him after they were concerned for his welfare.
Brown said officers found him "polite and courteous" and saw no reason to detain him on mental health grounds. He said he refused to "second guess" his officers' decision.
Among the victims was 20-year-old student Christopher Michael-Martinez, who was shot dead inside a deli. His room-mate tried to revive him but he died at the scene.
His father Richard Martinez, who spoke with his son 45 minutes before he died, told reporters: "Our family has a message for every parent out there - you don't think it will happen to your child until it does.
"Chris was a really great kid, ask anyone who knew him. His death has left our family lost and broken.
"Why did Chris die? Chris died because of craven, irresponsible politicians and the NRA (National Rifle Association). They talk about gun rights, what about Chris's right to live?
"When will this insanity stop? When will enough people say, 'Stop this madness, we don't have to live like this'. Too many have died. We should say to ourselves, 'Not one more'."
Eyewitnesses Alexander Mattera, 23, said: "We heard so many gunshots, it was unbelievable. I thought they were firecrackers. There had to have been at least like two guns. There were a lot of shots."
Shifman also said Rodger had received help from "multiple therapists", and said his social worker was sufficiently concerned about him to call the police just last week.
Rodger had been diagnosed with Asperger's syndrome, he said.
Shifman said it was a tragedy of "immense consequences" and that the Rodger family was co-operating fully with police.
Shifman said: "My client's mission in life will be to try to prevent any such tragedies from ever happening again.
This country, this world, needs to address mental illness and the ramifications from not recognising these illnesses."
He added that the family was "staunchly against guns" and supported gun-control laws. "They are extremely, extremely upset that anybody was hurt under these circumstances," he said.Suggest a correction