Los Angeles County sheriff's homicide detectives are investigating the shooting, which happened around 9 a.m. in the 900 block of Durfee Avenue.
Officials said the incident began with a call about a possible burglary at a vacant home where homeless have at times been spotted.
A relative of the home's owner noticed an open door and called 911, fearing a break-in.
When deputies arrived, they say they found a man and woman leaving the home. The woman stopped for the deputies, but the man, who was wearing a backpack, ran off on foot.
After a short foot pursuit, deputies said the suspect dropped his backpack and brandished two knives toward the deputies.
That was when one of the deputies fired and struck the 40-year-old suspect, who was later pronounced dead at the scene.
Only one deputy fired, but it was not immediately clear how many shots.
No deputies were injured in the incident.