The flight arrived from Melbourne at about 7:21 a.m.
The jet can carry 800 economy passengers or 555 first class passengers.
A few celebrities were on hand for the celebratory arrival. Olivia Newton-John and John Travolta were among the stars at the airport.
Travolta has an affinity for flying. When asked whether passengers could trust him in the pilot's seat of an Airbus A380, Travolta said, "Yes, you can trust me."
LAX spent nearly a billion dollars to accommodate the plane's size. According to the new owner of the jet, it's one of the most environmentally friendly planes in the air.
"Green, spacious and quiet," said Geoff Dixon, chief executive officer of Qantas Airways. "It's all those things, and a lot more. Qantas is the second-largest airline ordering the A380; we have 20 coming over the next few years."
Dixon said coming to Los Angeles for its inaugural flight was an easy decision to make because it's the entertainment capital of the world.
Lending their star power Monday were Olivia Newton-John and John Travolta, who is a commercial pilot. He was asked if passengers could trust him to fly the big Airbus.
"Would you fly here from Sydney?" asked one reporter.
"Would I? Of course, absolutely," answered Travolta.
"And I could trust you?"
"Yes, you can trust me," said Travolta.
The landing of the Airbus will hopefully help the local economy take off, according to Los Angeles Mayor Antonio Villaraigosa. According to airport officials, it could be a very soft holiday travel season.
How much does it cost for a ticket on the Airbus? Round-trip from L.A. to Melbourne: $1,100 for Economy class; a private suite with a double bed and video panels? About $27,000.
A second A380 aircraft is expected to be delivered to Qantas in November. At that time, Qantas will operate five A380 flights per week between Los Angeles and Australia -- two round-trip flights to Melbourne and three flights to Sydney.
LAX is expected to have 12 daily A380 flights by 2012 -- more than any other airport in North America.
The plane has a wingspan of more than 261 feet and can hold 82,000 gallons of fuel. Without fuel and passengers, the aircraft weighs 398 tons.
An economy ticket aboard the Airbus A380 is $1100 from LAX to Melbourne, Australia.