Meghan is said to be in 'good health' and they have had a successful 12 week scan - suggesting that the baby is due in late April, possibly around St George's Day.
It's been revealed they told the Queen and the rest of the royal family at Princess Eugenie's wedding, the Daily Mail reported.
Rumours were rife that Meghan may be pregnant after her mother Doria Ragland was seen taking baby-care classes in Pasadena with a view to looking after her new grandchild.
Royal sources have said her mother may move to London from the US to help her look after the baby because Meghan does not want to hire staff or a nanny after the baby is born and so is keen to fly her mother in to provide extra support.
Royal fans already suspected the Duchess was pregnant after she wore a suspiciously wide-fitting Givenchy coat to Princess Eugenie's royal wedding on Friday.
Many TV viewers were sure they could see a baby-bump beneath her long, navy blue coat as the Duchess was whisked into St George's Chapel, Windsor by her doting husband.
The new royal baby is expected to take the surname Sussex in the same way that Prince William's children, George, Charlotte and Louis have taken his title Cambridge as their last name at school and nursery.
In the same way, Princesses Eugenie and Beatrice have previously used the surname York, after their father's title Prince Andrew, the Duke of York.
Prince Harry and wife were seen holding hands when they arrived in Sydney early on Monday morning on a Qantas A380 flight from London via Singapore.
Earlier she sparked a storm of pregnancy speculation after she touched down in Sydney clutching two purple folders in front of her stomach.
Meghan Markle was seen holding the items in her right arm as she stepped off the plane on Monday morning with Prince Harry, leaving fans of the Royal couple guessing what information they could contain.
For many, the folders added to speculation Meghan Markle is expecting a baby, fuelling the fire already stoked by the large blue coat she wore at Princess Eugenie's wedding last week.
The couple returned to their own wedding venue at Windsor Castle on Friday but missed a lavish second day of celebrations on Saturday because of their flight to Australia.
- With Daily Mail
