At a news conference in Roseburg, they revealed that Chris Harper Mercer, 26, was enrolled in the class where the shooting took place.
They also said that 14 weapons were later found at his home.
Police earlier released the names of the victims, who ranged in age from 18 to 67. The oldest was a teacher.
President Barack Obama on October 2 expressed his anger at gun violence, calling on the public to press their politicians to support reform.
“The medical examiner has determined the cause of death of the shooter to be suicide,” Douglas County Sheriff John Hanlin told reporters on October 3.
He said that investigators were checking numerous leads and had already interviewed hundreds of people in the area.
On October 1, Chris Harper Mercer – dressed in a flak jacket – brought six guns to Umpqua Community College and opened fire.
The attacker killed eight students and a teacher.
He then killed himself after a gun battle with police officers who arrived at the college.
Chris Harper Mercer enlisted in the army in 2008, but was discharged after less than a month in basic training, for reasons unknown.
It is unclear why he carried out the killings. Two victims have said religion was an issue – the gunman asked his victims to state their religion and shot dead the Christians.
Chris Harper Mercer’s father, Ian Mercer, said he was “just as shocked as everybody” by his son’s actions.
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