"We would like to convey our deep appreciation to the government of Indonesia for its co-operation to facilitate the men’s return to Australia on humanitarian grounds," Mr Albanese, Foreign Minister Penny Wong and Home Affairs Minister Tony Burke said in a joint statement on Sunday.

"This reflects the strong bilateral relationship and mutual respect between Indonesia and Australia."

The five repatriated Australians were among nine arrested in 2005 after trying to smuggle heroin and had been behind bars serving life sentences in Bali.

Mr Albanese acknowledged the men had committed "serious offences" but said it was "time for them to come home".

"Australia respects Indonesia's sovereignty and legal processes and we appreciate Indonesia’s compassionate consideration of this matter," he said.

He said the government would "continue to co-operate" with Indonesia to counter narcotics trafficking and transnational crime.

"Australia shares Indonesia’s concern about the serious problem illicit drugs represents," he said.

Mr Albanese thanked President Prabowo Subianto for Indonesia’s co-operation and commitment to working with Australia on the men's return.

"I have conveyed my personal appreciation to President Prabowo for his act of compassion," he said.

Bali Nine ringleaders Andrew Chan and Myuran Sukumaran were executed in 2015, sparking a diplomatic incident with Australia, while Renae Lawrence was released in 2018 and Tan Duc Than Nguyen died of cancer the same year.

The Australian government had consistently advocated for the men and provided consular support to them and their families.

"We ask that the media respect the privacy of the men and their families at this time," Mr Albanese said.

Jakarta was reportedly seeking the repatriation of Indonesian prisoners held in Australia as part of any deal to bring the Bali Nine members home.

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