The couple, Harry and Meghan, who are on their first official overseas tour in Australia, New Zealand, Fiji and Tonga, are due to have a baby in the United Kingdom spring.
The Queen, the Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall and the Duke and Duchess of Cambridge are delighted for the couple, Kensington Palace said in a statement.
Prime Minister Theresa May said: "My warmest congratulations to the Duke and Duchess of Sussex on the happy news they are expecting a baby in the spring".
The royal couple started their official tour of Australia on Tuesday and were ferried across the harbour to greet cheering crowds packed in front of the Opera House, which was opened by Harry's grandmother almost nearly 45 years ago. She said that "I think it's lovely that they're having a family so soon".
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The baby will be seventh in line to become King or Queen, meaning the Royal couple have more freedom with their choice of first name.
The Duke and Duchess are touring Australia for the next nine days, primarily for the Invictus Games in Sydney.
The Duke and Duchess of Cambridge's first child Prince George arrived two years and three months after they Wednesday.
She showed a small baby bump as she received a stuffed kangaroo named Joey from Governor General Peter Cosgrove and his wife, Lady Lynne Cosgrove.
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Meghan said the koalas were "so, so sweet", while Harry reached out to pet one.
The news added further excitement to the royal fever already gripping the country, the paper says. "We thank them for coming to West Sussex and wish them every happiness with their first born". She said that "they certainly didn't waste any time, did they?"
Kensington Palace revealed that Harry and Meghan's first child is due next spring, on the eve of their first overseas tour together, with Meghan saying they are both "excited" about parenthood.
They are now on a tour of Australia, Fiji, Tonga and New Zealand. The couple had no official functions on Monday following the 17,140-kilometre flight that Qantas says takes 22 hours and 20 minutes. Prince Harry has been to all four countries, but on his own. "Looking forward to sharing in the joy during your stay down under", he tweeted on Monday evening. "I'm very happy to have a new son-in-law".
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