Police said Gene Evin Atkins, 28, was the man who held officers at bay for three hours on Saturday and engaged in a gunbattle in which the store manager was killed when she was caught in the crossfire.
Atkins was booked in the Los Angeles County jail on suspicion of murder. He could be arraigned as early as Monday and will likely face additional charges, a spokesman for the Los Angeles Police Department told ABC News.
He was being held on $2 million bail.
The slain manager of the Trader Joe's, located in the Silver Lake section of Los Angeles, was identified by her brother as Melyda Corado.
"I'm sad to say she didn’t make it. My baby sister. My world," Corado's brother, Albert Corado, wrote on Twitter late Saturday.
Albert Corado tweeted again on Sunday, saying he "missed his sister" and that their father was "doing his best to keep it together."
The Silver Lake store remained closed Sunday to give Corado's co-workers time to process the tragedy, the company said in a statement.
"Yesterday marks the saddest day in Trader Joe's history as we mourn the loss of one of our own," the company's statement reads.
The episode began around 1:30 p.m. on Saturday when Atkins got into an argument at a South Los Angeles residence with his grandmother and allegedly shot her seven times, police said.
The grandmother, whom relatives identified for ABC News as Mary Elizabeth Madison, was at a hospital in stable condition on Sunday.
After allegedly shooting Madison, Atkins shot and wounded a young woman, whose name was not released, at the South Los Angeles residence, forced her into his grandmother's car and drove off.
The car was equipped with LoJack tracking technology, which police used to locate the suspect, officials said. When police tried to stop the car a chase ensued, officials said.
During the high-speed pursuit, Atkins allegedly fired at officers, shattering the rear window of the car he was driving, police said.
He eventually crashed in front of the Trader Joe's and ran inside.
LAPD Chief Michel Moore told the Los Angeles Times that Corado was killed as she was exiting the store during the shootout. It is unclear if the fatal shot was fired by the gunman or a police officer, he said.
Police said Atkins was shot in the arm during the firefight.
Once inside the store, Atkins allegedly took shoppers and store employees hostage, police said.
Following a three-hour standoff, Atkins exited the store and surrendered to police.
At least six people, ranging from age 12 to 81, who were held hostage were treated at a hospital for non-life-threatening injuries.