The spacecraft that once reached 17,000 mph (28,160km/h) is trundling down the city’s famously low-level boulevards at a stately 2 mph.
“It’s pretty neat to see a spaceship in the street,” a spectator told local TV.
Endeavour began its 12-mile, two-day journey on Friday and is due to end up at the California Science Center.
The 75-ton spacecraft entered service in 1992, making 25 trips, logging 123 million miles and circling the globe almost 4,700 times.
Replacing Challenger, which was destroyed in an accident in 1986 that killed seven astronauts, Endeavour was the baby of the shuttle fleet.
NASA took its shuttles out of service last year in order to focus on destinations beyond low-Earth orbit, such as asteroids and Mars.
The three other surviving shuttles are already in museums or will be eventually:
• Enterprise is on display at the Intrepid Sea, Air & Space Museum in New York City.
• Discovery is on display at the National Air and Space Museum in Washington DC.
• Atlantis is due to be put on display at the Kennedy Space Center Visitor Complex in Florida.
For its trip across Los Angeles, Endeavour has been placed on a 160-wheeled carrier which is being guided by remote control.
The shuttle set off on Friday from Los Angeles international airport, where it arrived three weeks ago aboard a specially equipped Boeing 747.
After an early bumpy ride, it was backed into a shopping centre car park in the city’s Westchester neighborhood as crowds cheered.
Janet Dion, a family therapist from nearby Manhattan Beach, marvelled at the shuttle, its exterior weathered by its space missions.
“You can sense the magnitude of where it’s been,” she told the Associated Press news agency, looking at the heat tiles which had protected the craft on its returns to Earth.
Around midnight local time, Endeavour crossed a bridge over the Interstate 405 highway, an especially difficult part of the complicated journey because of the size of the shuttle and width of the bridge.
For the bridge manoeuvre, crews spent hours transferring the shuttle to a special, lighter towing dolly, which was then pulled across by a pickup truck.
Four hundred trees had to be cut down to make way for Endeavour’s wingspan. The city has promised to plant 1,000 replacements.
Power lines have also been raised and traffic lights pulled down but some stretches of the 12-mile journey are still a tight squeeze.
Former shuttle commander Mark Kelly, who captained Endeavour’s final flight, said he hoped the spacecraft would become an inspiration for future generations of astronauts.
“Maybe some day one of these kids that see Endeavour, look up at it at the California Science Center, will be that person that walks on the planet Mars?” he told US broadcaster CNN.
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