The transport is the largest object ever moved through the streets of Los Angeles.
The 12-mile slow trek started early Friday from Los Angeles International Airport.
More than 15,000 spectators attended a celebration outside the Forum arena in Inglewood where the spacecraft and its road crews enjoyed one respite Saturday morning, said police Lt. James Madia.
An afternoon stop in south Los Angeles will feature a performance produced by actor-choreographer Debbie Allen.
And it wouldn't be Los Angeles without a little product placement: A Toyota Tundra half-ton pickup truck pulled the shuttle Friday night over a bridge above Interstate 405. The shuttle and its transporter platform together weigh 170,000 pounds, or more than 80 tons.
In that feat, the highway to Los Angeles International Airport was shut down, preventing any motorists from possibly causing hazards by slowing down to photograph the spectacle, illuminated with stadium-strength spotlights.
Utility workers observed the procession while perched high in cherry pickers. Some power lines had to be temporarily disconnected, and crews were waiting to reconnect the overhead lines once the Endeavour passed through.
Turning corners was mesmerizing, especially in neighborhoods of single family houses.
In an Inglewood neighborhood at Crenshaw Drive and 84th Place, the shuttle faced one of its most challenging sections -- a residential street designed more for four wheels than two wings -- and was on a course to strike a tree.
But transportation crews maneuvered the vehicle, with little wiggle room, to spare the tree from a chainsaw. The shuttle cleared the 20-foot tree by a couple of inches.
The cutting down of trees has been controversial in some areas, but officials say they will plant two new trees for every felled one.
The spacecraft is expected to arrive late Saturday at the California Science Center, where it will be put on permanent display.
Officials planned the logistics of the move for months.
Endeavour, along with Discovery, Enterprise and Atlantis, became a museum piece after NASA ended its 30-year shuttle program in July 2011. All four shuttles have been permanently retired from service.
Named for the first ship commanded by British explorer James Cook, Endeavour rolled out of an assembly plant in Palmdale, California, in 1991 at a cost of $1.7 billion. It was the baby of the shuttle fleet, built as a replacement for Challenger, which exploded shortly after its 10th launch.
Over the next 20 years, Endeavour flew some of the highest-profile shuttle missions, covering nearly 123 million miles in 25 flights. It flew a Spacelab mission and numerous International Space Station assembly missions and rendezvoused with Russia's Mir Space Station.
The science museum has been trumpeting the arrival of the shuttle, saying on its website that it is building a new addition to its facility and plans to begin displaying Endeavour on October 30.