Karthik Rajaram, 45, left two suicide notes - one for police and one for friends and relatives - and a will.
The mother-in-law, Indra Ramasesham, 69, dead in bed on the first floor. Upstairs, police found a 19-year-old son, Krishna Rajaram, dead in bed in the master bedroom.
The gunman's 39-year-old wife, Subasri, was found in another room, also apparently shot while sleeping. In an adjoining room, a 12-year-old son, Ganesha, was dead on the floor, and his 7-year-old brother, Arjuna, was dead in bed. Coroner's assistant chief Ed Winter said the victims were shot multiple times.
A family friend had called police to the location because she had not heard from the wife, who was supposed to stop by her residence.
Moore said when no one responded to a door knock, officers went through the garage to get into the house. They first discovered the mother-in-law in bed with a gunshot wound to her head.
As police went through the house, they found the other bodies throughout the location, but they were not all found in bed. A recently purchased handgun was recovered at the scene.
There was no sign of forced entry into the home, Moore said, and the residence was in neat order.
Police also found three letters inside the home, allegedly written by the husband. One was addressed to law enforcement that attested to financial difficulties and took responsibility for killing his family members.
Another letter was a last will and testament, Moore said, and the third letter was a personal one to friends. Police did not release the details of the personal letter.
Moore said the suspect had been unemployed for the past several months and had no record of prior mental disabilities within Los Angeles County.
The father had a master's degree in business administration in finance, and formerly worked for PricewaterhouseCoopers and Sony Pictures, Moore said.
Police have interviewed neighbors, but no one reported hearing gunshots.
While police are unsure when the apparent murder-suicide occurred, neighbors said the last time they saw the husband was Saturday evening.
The crime scene is in a development of large, upscale homes about 23 miles northwest of downtown Los Angeles.
The investigation is ongoing.
Eyewitness News Reporters Carlos Granda and Robert Holguin contributed to this report. The Associated Press also contributed to this story.