The student was the son of Hollywood filmmaker Peter Rodger, who was assistant director on The Hunger Games.
At a news conference, police said Elliot Rodger had stabbed three male room-mates to death at his apartment.
He later went on a rampage through Isla Vista in a black BMW, shooting at people at random.
After exchanging gunfire with police, Elliot Rodger was found dead inside his crashed vehicle with a gunshot wound to the head, police said.
Santa Barbara County Sheriff Bill Brown said Elliot Rodger apparently killed himself during a shoot-out with police officers.
At a press conference, Bill Brown called it a “chaotic, rapidly unfolding convoluted incident” that involved multiple crime scenes.
Investigators are analyzing a YouTube video in which a young man who identifies himself as Elliot Rodger sits in a car and says he is going to take his revenge against humanity.
In a so-called manifesto published online, Elliot Rodger said he was born in London and spent the first five years of his life in Sussex.
“This was a time of discovery, excitement, and fun. I had just entered this new world, and I knew nothing of the pain it would bring me later on,” he wrote.
Sheriff Bill Brown said that after leaving his apartment, Elliot Rodger had gone to a sorority house, which houses female students, and hammered loudly on the door.
They did not open the door but Elliot Rodger had then shot three women in the street, killing two of them, Sheriff Bill Brown said.
Elliot Rodger then drove his car through the beachside community – which is near the University of California-Santa Barbara campus – targeting people at random, and the sixth victim was shot dead in a delicatessen.
Seven other people were wounded.
Sheriff Bill Brown said it was “very apparent” that the gunman was “severely mentally disturbed”, adding: “It’s obviously the work of a madman.”
He said authorities had recovered three semi-automatic handguns after Friday’s shooting.
All the weapons were bought legally and were registered to Elliot Rodger, the sheriff said.
Earlier, Peter Rodger’s lawyer, Alan Shifman, said that the “family believes the child was the perpetrator”.
He said Peter Rodger’s son had Asperger syndrome, had trouble making friends and had been receiving professional help.
Alan Shifman added that the family had contacted police about “recent posts on YouTube” by Elliot “regarding suicide and the killing of people”.
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