Klein Michael Thaxton, 22, surrendered just before 2 p.m., and the man he took hostage was unhurt, Police Chief Nathan Harper said.
The hostage-taking on the 16th floor of Three Gateway Center prompted an evacuation while Thaxton wrote on Facebook that he had "lost everything" and that people didn't have to worry about him anymore.
His friends responded by urging him to end the situation peacefully, including one who asked him to think of his mother.
A police spokeswoman identified the hostage as Charles Breitsman, owner of CW Breitsman Associates. The firm runs employee-benefits programs, but it wasn't immediately clear why he was targeted.
"(Thaxton) is a sick young man and we do need to take measures to see he is taken care of as well," police spokeswoman Diane Richard said. "We don't know if he's related to this company. We don't know what the tie-in is he has with this individual."
She said Breitman was able to meet with his family afterward.
"He is doing OK at this point, a little shaken up," Richard said, adding he was taken to police headquarters so that he could talk about the incident.
Police asked Facebook to take down Thaxton's page early in the afternoon in hopes of steering all of his attention to negotiations.
The Facebook exchanges had the potential to both help and harm the negotiations, Harper said. It's helpful that Thaxton can see "that people are concerned about his well-being," Harper said, but "it is a distraction for negotiating."
A worker on the 16th floor described a woman running into her office yelling for someone to call 911. Kathi Dvorak, an administrative assistant at AXA Advisors, said a second woman ran in and said her office was being robbed.
Harper had described the hostage-taker as having a military background but didn't elaborate.
Thaxton has a criminal record that includes a guilty plea to robbery earlier this year and a minimum six-month jail sentence.
Joel Kirchartz, a 28-year-old web developer who works on the 17th floor, said he and his co-workers looked out the windows Friday morning and "a bunch of cops pulled up with all sorts of sirens going; there must have been 20 of them." He said he went downstairs to find out what was happening and by the time he got outside, police had sealed the building.
Another worker, Sarah Vereb, said she was at her desk when she was ordered to leave the building shortly after a friend called to report that she wasn't being allowed up from the lobby.
Hundreds of workers walked down the stairwell. Vereb said the exodus was orderly and "very, very quiet."
A phone message left for the building's Santa Monica, Calif.-based ownership group was not immediately returned. The building complex management office confirmed the evacuation and said it was working with police.