Their first trip Down Under since the Coronation is due to take place in late October, around the time of their planned visit to Samoa for the Commonwealth Heads of Government Meeting.
It will mark 13 years since a ruling monarch has gone to Australia – Queen Elizabeth last visited in October 2011.
An Australian Government spokesman said: “The Prime Minister enjoys a warm relationship with the King, and looks forward to welcoming His Majesty to Australia.”
Charles and Camilla’s trip will coincide with Australia’s Bicentenary, marking 200 years of democracy.
But it may prove to be a significant test for the royals, amid rising republican sentiment.
The last referendum on the issue was in 1999, when 55% voted “no” to the question of ousting the monarch.
Mr Albanese voted in favour of a republic and before the Coronation, said: “I want to see an Australian as [our] head of state.”
However, since his nation’s rejection of a referendum to give more political rights to indigenous people, the premier’s intention to transition to a republic through another vote has been undermined.
Buckingham Palace declined to comment.