Santa Barbara County District Attorney Joyce E. Dudley described the deputies' actions in the confrontation on Oct. 15, 2019, as "justifiable homicide."
An investigation also found that Cameron Ely, 30, stabbed his mother, 62-year-old Valerie Lundeen Ely to death shortly before he was shot at the family's home near Santa Barbara.
Authorities said the deputies found Cameron Ely outside the home, and he told them he had a gun and that he moved his hands as if he were grabbing a weapon. The deputies then opened fire.
No weapon was found.
'Tarzan' actor Ron Ely's son unarmed when deputies fatally shot him in Santa Barbara
Last week, Ron Ely filed a lawsuit over the deaths of his wife and son against Santa Barbara County, the Sheriff's Office and four deputies.
Ron Ely played the title character on the NBC series "Tarzan," which ran from 1966 to 1968. Ely also hosted the Miss America pageant in 1980 and 1981. He had retired from acting in 2001, although he did have a role in a television movie in 2014.
The home on Mariposa Drive is in the exclusive Hope Ranch community on the Santa Barbara coast.
The Associated Press contributed to this report.