The announcement came as Harry and the former Meghan Markle arrived in Sydney at the start of a 16-day visit to Australia, Fiji, Tonga and New Zealand. Hundreds of people gathered to catch a glimpse of the couple after they landed.
"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," the palace said in a statement.
The trip will include attending the Invictus Games, a visit to a Sydney zoo and visit the rural Flying Doctor service.
The prince and the former actress married in a glittering service in Windsor in May.
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