Prince George was in his mother’s arms as the royal couple emerged from a plane at Kingsford Smith Airport.
Kate Middleton carried the 8-month-old down the steps of the aircraft before she and Prince William were met by dignitaries.
The Duke and Duchess of Cambridge will spend 10 days travelling across Australia, visiting its famous sites and honoring its war dead.
Australia’s PM Tony Abbott and Governor-general Peter Cosgrove, their spouses and other figures were among those who met Prince William and Kate Middleton as they descended from the plane.
Kate Middleton, wearing a yellow dress by Roksanda Ilincic, handed Prince George to his father as she accepted flowers from Joscelyn Sweeney, a 22-year-old with Down’s syndrome.
A lively Prince George, dressed in a white cotton babygrow with ships on the front, touched hands with the governor-general’s wife Lynne Cosgrove before his parents left for their first engagement at the Sydney Opera House.
Prince William and Kate Middleton completed the first leg of their trip Down Under with a tour of New Zealand.
They arrived in Australia on Wednesday for the second leg as a political scandal erupted, forcing one of the country’s senior figures to pull out of the official greeting party.
Barry O’Farrell resigned as premier of New South Wales just hours before Prince William and Kate Middleton arrived after a document emerged contradicting evidence he gave to an anti-corruption inquiry.
He admitted to a “massive memory fail” after he failed to declare a gift of A$3,000 wine.
The leader of the New South Wales Liberal Party had told an inquiry that he never received the wine and that he could not remember calling businessman Nick Di Girolamo, who sent him the gift in 2011.
Barry O’Farrell resigned after investigators unveiled a hand-written thank you note from him.
He had been due to greet the royal couple on the tarmac, and later at their visit to Sydney Opera House, but did not attend the welcome ceremony at the airport.
Barry O’Farrell was not replaced by another official.
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