The victims were Wayne Chan, 56, and Benson Louie, 50, both of San Francisco; and 46-year-old Michael Lefiti of Hercules, California, the city's medical examiner said.
Two others were shot but survived the Wednesday shooting at the UPS San Francisco Customer Center, police said.
Officers responded to a report of an active shooter about 8:55 a.m. local time (11:55 a.m. ET) at a package sorting and delivery facility, a couple of blocks east of Franklin Square.
When officers went inside the building, they found the suspect armed with an assault pistol, Assistant Police Chief Toney Chaplin told reporters.
"The suspect put the gun to his head and immediately discharged the weapon," he said. No officer fired a shot during the confrontation, Chaplin said.
UPS spokesman Steve Gaut released a statement saying that six employees were involved in a "shooting incident" but that the company, which employs 350 people, could provide any identifications until the police investigation is complete.
The suspect was wearing a UPS uniform but investigators have not confirmed whether he was an employee. A source close to the investigation said he worked for the delivery company.
Authorities didn't know if the shooter have targeted victims. On Wednesday, Chaplin said there was no indication the shooting was terror-related but did not talk about a possible motive.
Five other people were injured, likely during the evacuation, Chaplin said.
Authorities interviewed all witnesses and were talking to the victims' families on Wednesday.
'Run, there is a shooter'
A woman named Michelle, who did not want to provide her last name, was walking to work across the street from a UPS facility when she saw several UPS employees running down the street. They told her to run because there had been a shooting, she told CNN, explaining she ran about a block with the workers.
"I was confused. They crossed the street and when they got to me, they said, 'Run, there is a shooter,' so I started to run with them," she said. "Several of them said it was a driver they worked with who had a gun and opened fire. I feel terrible for the people hurt and for the UPS team that was there but survived."
Antonio Salic told CNN he was working in a house across from the UPS building when he heard shots fired.
"I peeked out the window," he said. "I saw people getting out (of the building), and they were wounded. A lot of people were running."
The construction worker said he also saw people on the roof with their hands up, letting police know they were unarmed.
"Police approached and they were taken to a safe place," he said.
After the shooting, UPS said the company wasn't immediately sure of the status of the survivors who were taken to the hospital.
"The company is saddened and deeply concerned about affected employees, family members and the community we share," a statement said.
Aerial footage showed police leading dozens of people, many in matching brown work uniforms, out of a building. A tactical vehicle arrived shortly thereafter.
The site of the shooting was in the Potrero Hill area, a largely residential neighborhood. The shooting was also not far from a Whole Foods market and the brewery that makes Anchor Steam beer.
Residents were warned to avoid the area because of heavy law enforcement activity.