The victim was identified as Anthony Rivera, 48, of Los Angeles.
The hijacking occurred about 12:45 a.m. Wednesday near Manchester Avenue and Figueroa Street, according to the LAPD.
The bus was pursued by authorities from South L.A. to downtown, where SWAT officers arrested the suspect. Paramedics took the wounded man from the bus to a hospital, where he died.
Another passenger and the bus driver were rescued.
Police arrested 51-year-old Lamont Campbell of Los Angeles, who remains in custody. A case against him will be presented to the district attorney's office on Monday, the LAPD said.
Rivera lived just a few blocks from the area where Campbell initially got on the bus. Friends are remembering him as an outgoing, friendly man who always looked out for others.
"I knew Anthony for over three years," said Brian Kitchen. "He is a standup guy. He was my assistant manager here at the house, he was really good. He would help me set up the tents, help me sell stuff, whatever I needed help with, he would help."
Rivera's friends said he wasn't the type of man to sit back and let bad things happen.
"I wouldn't be surprised if Anthony stood up to the person who had the weapon on the bus, because that's the type of person he was," said Michael Johnson, a friend of Rivera's.
Wednesday's shooting and hijacking is the latest in a series of violent attacks on the transit system and has renewed safety concerns on Metro buses and subways.
Metro says it's working on a new weapons-detection system and other safety measures.
"I think it's kind of sad that is happened on a bus like that," said Kitchen. "I think more security needs to be done, something needs to be done about that public safety, because it's not safe."
City News Service contributed to this report.