The royal couple arrived in the harbour city on Monday morning (local time) with a 10-person entourage as part of their 16-day tour of Fiji, Tonga and New Zealand between Tuesday, October 16 and 31.
It comes on the 25th anniversary of the late Princess Diana and Prince Charles travelling down under on their first tour.
The royal couple reportedly flew in on a Qantas A380 from London via Singapore.
They were said to have been greeted by a heavy police presence at Sydney Airport before making their way to Admiralty House, the Governor-General’s Sydney residence.
Meghan and Harry’s official duties do not start until Tuesday, so the couple have a low-key start to their busy tour.
It comes after the pair attended Harry’s cousin Princess Eugenie’s Royal Wedding on Friday, with celebrations continuing over the weekend.
Prince Harry’s parents travelled to Alice Springs, Uluru/Ayers’ Rock and Sydney when Prince William was just a baby.
Princess Diana and Charles also appeared on the famous Bondi beach during the 41-day trip.
Once in New Zealand, Meghan and Prince Harry will also will tour the capital of Wellington, Auckland and Rotorua before heading to Abel Tasman National Park in the South Island.
Charles and Diana also visited Auckland and the Bay of Islands.
Starting on Tuesday, Harry and Meghan Markle will take part in 76 engagements over their 16-day trip to the Pacific region.
The tour coincides with the Invictus Games in Sydney, which run from October 20 to October 28.
The sporting event – founded by Prince Harry in 2014 – gives sick and injured service personnel and veterans the opportunity to compete in sports such as wheelchair basketball and sitting volleyball.
After landing in Sydney, the duke and duchess will travel to Dubbo and Melbourne, before spending three days in Sydney from October 19-21 to mark the launch of the games. They will return for the closing ceremony.
However, sport is not the sole focus of the trip.
While in Australia, Harry and Meghan will also visit organisations including schools and a rural Flying Doctor service, greet members of the public at the Sydney Opera House, and meet young leaders and community members at Government House.
After Australia, the couple will fly to Fiji, where they will be greeted with an arrival ceremony similar to one attended by the Queen and Duke of Edinburgh in 1953.
In Fiji, Prince Harry will pay tribute to Fijian war veterans and the couple will attend a state dinner, before flying to Tonga.
The tour will conclude with a four-day trip to New Zealand, where they will be greeted by Prime Minister Jacinda Ardern.
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.
Harry and Meghan will return to London from Auckland on November 1.
Kensington Palace said: “There is a long history of friendship between the Royal Family and Australia, Fiji, Tonga and New Zealand, and their links with the UK are extensive.
“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.”