Duke of Cambridge: Australia a beacon of confidence
The Duke of Cambridge has described Australia as a "beacon of confidence" as he and his family began the next leg of their Antipodean tour.
Thousands turned out to greet the royal couple at Sydney Opera House to mark the start of their 10-day visit.
In a speech, the duke also spoke of the Queen's affection for Australia and praised the nation's creativity.
William, Kate and Prince George arrived in Sydney earlier on Wednesday, having completed a tour of New Zealand.
Speaking at the couple's first engagement, the duke said he and his wife had been looking forward to the visit for a long time.
"Her Majesty spoke recently of how, since her first visit here 60 years ago, she has been privileged to witness Australia's growing economy and flowering self-confidence," he said.
"For Catherine, Harry and me, born in the early 80s, we've never known anything else - Australia and Australians have always been for us a beacon of confidence, creativity in the arts and sporting ability."
William said Prince George had begun forging his own link with Australia.
"Catherine and I were very grateful for the many kind messages and gifts from across the country that we received when George was born," he said.
The duke and duchess are expected to bring the eight-month-old prince to Taronga zoo in Sydney on Sunday where an enclosure housing bilbys - a rabbit-like marsupial - will be named after him.
William added: "I suspect George's first word might be 'bilby' - only because koala is harder to say. We really look forward to our time here together as a family."
Earlier, Prince George was in his mother's arms as the royal couple emerged from a Royal Australian Air Force plane at Kingsford Smith Airport.
Kate carried him down the steps of the aircraft before she and William were met by dignitaries.
Australia's Prime Minister Tony Abbott and governor-general Sir Peter Cosgrove, their spouses and other figures were among those who met the royals as they descended from the plane.
The duchess, wearing a yellow dress by Roksanda Ilincic, handed George to the duke as she accepted flowers from Joscelyn Sweeney, a 22-year-old with Down's syndrome.
A lively George, dressed in a white cotton babygrow with ships on the front, touched hands with the governor-general's wife Lynne before his parents left for their first engagement.
The family will spend 10 days travelling across Australia, visiting its famous sites, honouring its war dead and meeting locals.
They arrived in Australia 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 the duke and duchess arrived after a document emerged contradicting evidence he gave to an anti-corruption inquiry.
Mr O'Farrell 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.
He resigned after investigators unveiled a hand-written thank you note from him.
Mr O'Farrell 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.
He was not replaced by another official.