Kensington Palace has announced on Twitter that the couple, who wed in April 2018, are expecting a baby early next year.
The child will be seventh in line to the British throne, after Prince Charles, Prince William, his three children and Prince Harry.
The royal pair have just touched down in Sydney, Australia on their first official tour as a married couple.
They will also visit New Zealand, Fiji and Tonga and will officially open the Invictus Games.