The announcement came as Meghan, 37, and Prince Harry, 34, arrived in Sydney on Monday ahead of a 16-day tour of Australia and New Zealand.
Their baby will be nineth in line to the throne.
The Queen and other senior royals were told about the pregnancy on Friday, when members of the Royal Family gathered
Meghan – who has had her 12 week scan – attended the wedding with Prince Harry, wearing a long, dark blue coat, which 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 tour, which will also take in Fiji and Tonga.
It is their first official royal tour since their wedding, which also took place at St George’s Chapel, Windsor.
Their first engagement is on Tuesday, when crowds of wellwishers are expected to congratulate the couple.
The duke and duchess 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.