The baby will be seventh in line to the throne.
Harry and Meghan had just touched touched down in Australia for their first overseas tour as a married couple when the news broke.
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Meghan will be taking her best friend and stylist Jessica Mulroney with her when they travel around Australia this month.
Kensington Palace announced the news on Monday morning. A Palace spokesperson said: "Ms. Ragland is very happy about this lovely news and looks forward to welcoming her first grandchild".
Later this week Prince Harry and the Duchess of Sussex will move on down to Melbourne where they will be received by the state's politicians, meet youth leaders and take in the sites the city has to offer, including riding a tram.
Meghan, 37, and Harry, 34, were married in St. George's Chapel at Windsor Castle.
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.
However, it is thought Meghan has taken advice about the tour and made a decision to continue to both Fiji and Tonga, although she is expected to skip a couple of outings in Fiji. But now, everyone wants to know whether their future children will be handed similar titles by the Queen.
For example, as the son of the Duke and Duchess of Cambridge, Prince George uses Prince William and Kate Middleton's dukedom, Cambridge, as his last name at school.