The King will attend a Sydney church service to begin the monarch's first tour of Australia since his accession to the throne.
Charles and Camilla's official engagements in the country will start with a trip to St Thomas' Anglican Church for a service led by Archbishop Most Reverend Kanishka Raffel.
Security arrangements for Sunday suggest the couple will meet wellwishers afterwards.
They landed in Australia on Friday before the Queen met a 12-year-old boy with a serious blood condition.
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Ky, who suffers from aplastic anaemia, gave her flowers after she disembarked the plane at Sydney Airport - fulfilling his dream to meet a member of the Royal Family.
Shortly afterwards the Sydney Opera House was lit up with a four-minute projection of photographs of the King and Queen to mark their arrival.
They then met Australian Prime Minister Anthony Albanese and his fiancee Jodie Haydon and Australia's governor-general Sam Mostyn.
A picture was released of the couple at the governor-general's official residence Admiralty House as they had a rest day on Saturday.
Their six-day visit only has two-and-a-half days of official engagements to allow the King enough rest time amid his cancer treatment.
Ahead of the tour the King was given the honorary ranks of Admiral of the Fleet, Field Marshal, and Marshal in three services of the Australian Defence Force (ADF).
The appointments were made by the governor-general, who said they represent an important symbol of connection between the UK and Australia.
To mark the tour, the Association of Commonwealth Countries (ACU) also announced its own King's Commonwealth Fellowship Programme.
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The new scheme will offer fellowships, undergraduate scholarships, and funded PHDs aimed at solving the economic, social, and environmental crises faced by small island developing states (SIDS).
The Commonwealth has 25 small island developing states, including Fiji, Kiribati, Nauru, Papua New Guinea, Samoa, Solomon Islands, Tonga, Tuvalu, and Vanuatu.
King Charles said he was "delighted" to have inspired the new initiative.
"There is so much we can learn from one another as we work together within the Commonwealth to tackle the major challenges of our age and, as these fellowships do in small island developing states, to address them where they are felt most acutely," he said.
"It is my fervent hope that these new fellowships will play a significant role in furthering the free exchange of knowledge and advancing the spirit of mutual support that lies at the heart of our Commonwealth - today, tomorrow and towards a brighter future for all."