The man, identified by a relative as Ugandan native Alfred Olango, 30, was shot on Tuesday in the San Diego suburb of El Cajon after police received a call about a man behaving erratically and walking in traffic.
El Cajon police chief Jeff Davis said Olango had ignored repeated calls by officers to remove his hand from his pocket and one officer used a Taser against him while another fired his weapon as they felt threatened.
"At one point, the subject rapidly drew an object from his front pants pocket, placed both hands together and extended them rapidly toward the officer taking up what appeared to be a shooting stance," Davis said in a statement. "At this time, the officer with the electronic control device discharged his weapon.
"Simultaneously, the officer with the firearm discharged his weapon several times, striking the subject."
"This will be transparent. This will be looked at by multiple sets of eyes, and not just ours," he vowed at a news conference.
Following the shooting, several people gathered at the scene Tuesday night chanting "black lives matter" and "hands up, don't shoot."
One woman posted a Facebook Live video after the shooting that showed a distraught woman who identified herself as Olango's sister and said she had called police to help her brother who was mentally ill.
"You guys came and killed my brother," the woman wails in the video that had been viewed 82,000 times by Wednesday morning.
"I called you guys to help my brother. You killed my brother in front of me."
Witnesses said they heard five shots as police confronted Olango.
Davis said the two officers involved in the shooting, each with more than 20 years of service, had been placed on administrative leave pending the investigation.
Police have also released a still photo lifted from a video taken at the scene that shows a man in a shooting stance.
The deaths of black men at the hands of police have spurred protests across America, most recently last week in the North Carolina city of Charlotte.
The fatal shooting of Keith Lamont Scott, 43, triggered days of unrest, forcing the governor to declare a state of emergency and deploy the National Guard.