The Boeing 787-9 Dreamliner completed the 9,226-mile journey to arrive slightly earlier than the scheduled arrival time 5.10am.
Auckland is also the origin of Emirates Airline Flight 449, with Airbus A380 superjumbos travelling almost 14,200km to Dubai.
Qantas chief executive Alan Joyce said it was a "historic day for aviation", adding he was really excited.
The new Perth-London flight is around three hours faster than other routes that involve stops in the Middle East to change planes or refuel.
Qantas said its customers can choose from three routes between Australia and London - the direct Perth-London service on the Dreamliner; a reinstated Sydney-Singapore-London service on the A380; and via Brisbane, Sydney, Melbourne, Adelaide and Perth to London via Dubai with partner Emirates on mix of A380 and 777 aircraft.
The maiden flight of a new nonstop regular passenger service between Australia and Britain has touched down at London's Heathrow Airport.
Qantas is using a Boeing 787-9 Dreamliner, which is twice as fuel-efficient as the usual Boeing 747.
Qantas Group CEO Alan Joyce celebrates as he arrives at Heathrow Airport
The former champion, Singapore Airlines' 15,300km Singapore-New York route, was discontinued in 2013.
Some of the passengers have agreed to share data on their sleeping and activity patterns with researchers from the University of Sydney.
The plane was fitted with special features to minimise discomfort during the journey including measures which minimised noise.
Western Australia's state government is also hoping to see an increase in tourist numbers as a result of the new direct route.
Qantas chairman Alan Joyce said the Australian airline had been preparing for this first direct nonstop flight ever since the airline was founded in 1921.
In a Twitter post, Qantas said the flight was led by Captain Lisa Norman, Captain Jeff Foote, First Officer Dave Summergreene and Second Officer Troy Lane.
The airline unveiled plans for the world's longest non-stop commercial flight, for the "last frontier of global aviation", back in August previous year.