Kensington Palace confirmed the news on its official Twitter account today.
The message, posted over several Tweets, said: "Their Royal Highnesses The Duke and Duchess of Sussex are very pleased to announce that The Duchess of Sussex is expecting a baby in the Spring of 2019.
"Their Royal Highnesses have 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."
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Millions watched as the royal couple wed in May this year, with a grand, star-studded ceremony at St George's Chapel, Windsor Castle.
The new baby will fall seventh in line for the throne, bumping Prince Andrew, Duke of York, into eighth place.
It's unlikely that the baby will ever be monarch, having three cousins further up the line of succession - Prince George, Princess Charlotte and Prince Louis.
Due to George V's decision to limit titles within the royal family in 1917, it is unlikely that the baby will be a princess or princess.
A son would be known as Earl of Dumbarton - because a first son of a duke is allowed to use one of his father's other lesser titles as a courtesy title.
Harry was also made the Earl of Dumbarton on the morning of his wedding, as well as being given a dukedom.
A daughter would be Lady (first name) Mountbatten-Windsor.
But, this could change.
The Queen stepped in ahead of George's birth to issue a Letters Patent to ensure the Cambridges' children had fitting titles, but this royal baby is much further down the line of succession.
Meghan is planning to become a British citizen - but it is not known whether she will hold dual nationality, and at present is still a US citizen.
Harry and Meghan could apply for their child to have dual US-UK citizenship.
According to the American Embassy in the UK, a child born outside of the US and in wedlock to a US citizen parent and a non US citizen parent, may acquire US citizenship at birth if the US parent lived in America for five years - two of which were after the age of 14.