"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 tweeted.
They also mentioned Meghan's mother.
The mum-to-be wore a white dress, made by a local Sydney designer for the first official day of their Australian tour.
Meghan said the koalas were "so, so sweet", while Harry reached to pet one of the animals and asked about their diet and sleeping habits.
Many others in the Australian capital have told Vigliotti how inspired they were by the royal couple, specifically all the charity work they do for mental health organizations and their role in the Invictus Games, for wounded veterans.
The Duke also opened the Taronga Institute of Science and Learning before the couple took a boat ride across the harbour to the Opera House.
Kensington Palace said in a statement: "There is a long history of friendship between the royal family and Australia, Fiji, Tonga and New Zealand, and their links with the United Kingdom are extensive".
Harry was reunited with an old friend, 98-year-old Daphne Dunne who he first met in 2015.
Dunne then said, "I think it's wonderful the two of you". The governor-general, who represents Queen Elizabeth II, Australia's head of state and Harry's grandmother, sent staff to hastily buy a toy kangaroo with a joey in its pouch and a tiny pair of Australian sheep skin boots for their pregnant guest.
On Wednesday, October 17, the Royals will fly to Dubbo in order to meet with the Royal Flying Doctor Service and farmers struggling with persistent drought.