A statement from Kensington Palace said the baby is expected in the spring of 2019.
All eyes have been on Harry and Meghan since they tied the knot in May, and speculation has been rife in recent days that the newlyweds were expecting their first child together just a few months after marrying.
Kensington Palace announced that the trip would coincide with the Invictus Games, which is being held in Sydney from October 20-27.
The prince and the former actress married in a glittering service in Windsor in May.
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Betway has already revealed the baby name odds, with spokesperson Alan Alger saying: "Royal baby fever is back again and the betting on Harry and Meghan's first baby is up and running with plenty of interest".
Prince Harry and Meghan just days earlier at Princess Eugenie's wedding.
The newly expectant couple recently arrived in Sydney for the first stop of a 16-day tour of Australia and the South Pacific.
And now they're starting a family!
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The royal couple will journey to Cockatoo Island and the Domain for Invictus events over the weekend before taking off to Fraser Island on Monday where they'll meet local elders and learn about Australia's indigenous history. Queen Elizabeth II is the titular head of state in the country, but the population has always been divided over whether to cut its ties with the British monarchy.
Britain's Prince Harry, Duke of Sussex, (R) and Meghan Markle, Duchess of Sussex, (L) leave Windsor Castle in Windsor on May 19, 2018, in an E-Type Jaguar after their wedding to attend an evening reception at Frogmore House.
The couple first began dating in 2016 and announced their engagement in November 2017.
The trip, their first outside the United Kingdom and Ireland, will officially begin on Tuesday and will see the couple watch the Invictus Games, visit a Sydney zoo and visit the rural Flying Doctor service.
"I'm sure she's with us yeah, you know, jumping up and down somewhere else", Harry shared.
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Lately, there had been talk of a new owner turning it into a community center, the Detroit News reported . "If I had them in the funeral home then my funeral home wouldn't smell fresh", Cantrell told Fox.
Sky News royal correspondent Rhiannon Mills is in Australia with the couple and said: "This tour was going to be busy enough - I think this is going to bring another exciting focus to it all".