The news has been announced as she and Prince Harry begin a tour of Australia.
Kensington Palace said the couple "appreciated all of the support they have received from people around the world since their wedding in May and are delighted to be able to share this happy news with the public".
The baby will be seventh in line to the throne.
The duke and duchess had last been seen at Princess Eugenie's wedding in Windsor on Saturday, when Meghan's outfit of a long, dark blue coat sparked speculation she could be expecting.
That speculation intensified when she was seen clutching two large folders in front of her stomach as she arrived in Sydney for the 16-day trip to Australia, Fiji, Tonga and New Zealand.
It's their first official royal tour since they got married five months ago.
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