Despite the almost 20-hour flight from London to Australia, both royals looked fresh-faced and happy to kick off their 16-day tour of the continent, which will take them across Australia, Fiji, Tonga and New Zealand.
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.
This is Harry and Meghan's first overseas tour as a married couple.
Tomorrow the Duke and Duchess will be given an official reception at the home of the Governor General of Australia, Sir Peter Cosgrove, where they will also meet representatives from the eighteen countries taking part in the Invictus Games in Sydney.
The Duke and Duchess of Sussex have arrived at Admiralty House in Sydney for a day of rest before they begin an intense 16-days of engagements across four countries.
Storm Isaac to weaken gradually over next few days: NHC
Isaac is forecast to gradually weaken over the next few days, and could degenerate into a tropical wave at any time. At another gas station, a long line of vehicles followed a tanker truck that pulled in with 8,800 gallons of fuel.
Their tour will end with a four-day trip to New Zealand, where they will be greeted by Prime Minister Jacinda Ardern, who recently became the second ever elected head of state to give birth while in office.
The Duke and Duchess of Sussex are to ride a ferry across Sydney Harbour past the Opera House on Tuesday, as well as watch an indigenous contemporary dance troupe and see koalas at the Taronga Zoo.
The Olympics-style sporting event was founded by Prince Harry in 2014, for sick and injured veterans.
Just over a year ago, the royal couple was spotted holding hands for the first time in September 2017, when they attended last year's Invictus Games in Toronto, Canada.
New South Wales (NSW) Premier Gladys Berejiklian welcomed the couple to Australia, describing the visit as exciting.
The couple will mark the games' launch and closing ceremony in Sydney.