Meghan and Harry reportedly flew in on a Qantas A380 from London via Singapore.
Harry and Meghan were driven from the airport to Admiralty House, the official Sydney residence of Governor General Peter Cosgrove, who represents Australia's head of state, Queen Elizabeth II, Harry's grandmother.
The Daily Mail and The Sunday Times both report that Mulroney will be on hand with her husband, Ben, in an "unofficial capacity"-reportedly meaning they'll be paying their own way and kind of just casually tagging along on the royal tour, NBD".
Hundreds of well-wishers gathered with umbrellas outside the airport and Admiralty House in the hope of catching a glimpse of the couple.
They will then return to Australia for a few days before the annual Invictus Games in Sydney - an annual event created by Prince Harry in 2014, similar to the Paralympics, in which wounded or disabled military personnel and veterans compete in a variety of sports.
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New South Wales (NSW) Premier Gladys Berejiklian welcomed the couple to Australia, describing the visit as exciting.
The duke and duchess will learn about environmental challenges while in Wellington, visit a charity which supports children with parents in prison, and meet members of the public in Auckland and Rotura.
They are also scheduled to visit New Zealand and Tonga.
"The duke and duchess are very much looking forward to experiencing the unique cultures and customs of those four Commonwealth countries and have asked that this tour allow them opportunities to meet as many Australians, Fijians, Tongans, and New Zealanders as possible".