A beaming Meghan Markle looked remarkably unfatigued by a 22-hour flight as she walked out of Sydney's airport with Prince Harry on Monday for a rest day before they officially start a 16-day tour of Australia and the South Pacific.
A statement from Kensington Palace said the baby is expected in the spring of 2019.
Kensington Palace said the couple were "delighted to be able to share this happy news with the public".
The couple follow in the footsteps of Prince Harry's parents - Prince Charles and Diana, Princess of Wales - whose first royal tour was to Australia and New Zealand.
The prince and the former American actress landed on an overcast morning after a commercial flight from London with a brief stopover in Singapore. Meghan, wearing skinny black trousers and a black, burgundy trimmed coat, was smiling and clutching folders, while Harry gave a thumbs up to bystanders.
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Prince Harry, Duke of Sussex and Meghan, Duchess of Sussex leave Windsor Castle in the Ascot Landau carriage during a procession after getting married at St Georges Chapel on May 19, 2018 in Windsor, England.
The royal couple waved as they drove through the gates of the governor-general's residence in Kirribilli, just after 8am.
The tour coincides with the Invictus Games in Sydney, which kicks off on Saturday and runs for a week.
She had said, in a 2016 interview, that becoming a mother was on her "bucket list", while Harry said in their engagement interview: "You know, I think one step at a time, and hopefully we'll start a family in the near future".
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The couple will attend the games' launch and closing ceremonies.
Australian Prime Minister Scott Morrison, who took the top job in August after a backbench revolt ousted predecessor Malcolm Turnbull, is a constitutional monarchist.
Harry and Meghan will be spend three days in New Zealand, beginning in the capital Wellington on October 28.
Harry, 33, had recently joked he didn't want a large family. "I'm very happy to have a new son-in-law".
There was widespread speculation Meghan was expecting a child after she wore a long, dark blue coat to the wedding of Princess Eugenie and Jack Brooksbank in Windsor on Friday.
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