The so-called Millennium Hollywood project envisions two towers of 30-plus stories adjacent to the landmark Capitol Records building.
City News Service reports that the council gave unanimous 13-0 approval Wednesday.
Some Hollywood groups have campaigned against the project on grounds that it would be a monstrosity and worsen traffic congestion.
Opponents have also charged that the site is on an active earthquake fault.
The project includes residential units, hotel rooms, restaurants and other retail space.