Zumthor has designed a 37,000-square-metre building for the art museum, also known as LACMA.
Images show the structure's dark-coloured curving form raised on chunky supports, allowing it to snake over the busy Wilshire Boulevard.
The vertical elements will provide access to the main galleries above, and also protrude through the sprawling horizontal volume.
Windows around the tops of these elements will help bring natural light into central areas of the museum.
The latest floor plan shows eight "anchor" galleries spread across the length of the building.
One will be located on the south side of Wilshire Boulevard, while the other seven will all be positioned in the section to the north of the bridge galleries crossing the street.
The two principle entrances will be located on either side of the road.
A curve in the building will create a semi-enclosed area for displaying sculptures and for visitors to congregate.
Zumthor drastically modified his plans for LACMA in 2014 to prevent damaging the nearby La Brea Tar Pits that inspired his design.
His original proposal, unveiled the previous year, involved the demolition of four buildings on the site, but encroached too closely on the pits – sparking a petition to alter the scheme.
This resulted in the more snaking form that branches across the boulevard, which was simplified further in 2015 to be less curvaceous.
"I started out trying to come up with a shape that would work for the whole site and maybe even for the whole city," said Zumthor, speaking to the LA Times at the time. "The forms were trying to arrange themselves softly, maybe biomorphically. And then it had to stretch over the street."
"The shape has developed more character and self-assurance," he added. "I still want it to be friendly to the site — but at the same time have a strength of its own."
The latest iteration was praised by the campaigners, LACMA director Michael Govan and the mayor of Los Angeles.
However it was criticised by LA Times critic Christopher Hawthorne, who described it as "the product not so much of boldness as a combination of diplomacy and fidelity — perhaps misguided — to certain elements of his original design".
Zumthor has been working on the project since 2008, but construction is not due to commence until 2018.