The announcement came after investigators released a man who had been detained as a “person of interest”. Police spokesman Sergeant Richard Lewis said that the man was questioned and released and was no longer a suspect.
The violence began when the gunman opened fire on a house where two bodies were later found. Officials said they were his father and brother.
Police eventually shot the man dead in the library at Santa Monica College.
Officials said the killings began as a domestic violence incident. As the house burst into flames, the man wounded a woman in a car before he moved toward the campus, spraying bullets as he went.
Police said he then opened fire on a bus, a police car and other vehicles, and passers-by. The driver of a sports utility vehicle leaving a car park was killed and two passengers wounded as the car crashed through a wall.
From there, the gunman entered the campus, fatally wounding a woman as he made his way toward the library, where students were studying for final exams.
“The officers came in and directly engaged the suspect and he was shot and killed on the scene,” said police chief Jacqueline Seabrooks.