The council, in a 13-0 vote Wednesday, allowed developer Millennium Partners to build two skyscrapers and more than 1 million square feet of office, hotel and retail space on several vacant parking lots.
The lots surround the Capital Records building, the Los Angeles Times said, and the towers will be 39 and 35 stories tall.
Mayor Eric Garcetti said he plans to sign the $664 million project.
Opponents of the project attempted to get the project delayed, the Times said.
Residents argued that the skyscrapers are out of scale with the surrounding buildings and will add to traffic problems.
John Parrish, head of the California Geological Survey, also sent a letter to the council, saying the skyscrapers may fall in an earthquake fault zone.
The city's Department of Building and Safety asked the developer to conduct a second seismic test at the site.
Millennium co-founder Philip Aarons said the company hopes to break ground within a year but the project could be delayed if the opponents sue.