The five remaining members of the Bali Nine jailed for life over a drug smuggling plot have returned to Australia under a deal negotiated with the Indonesian government, describing themselves as “relieved and happy”.

The prime minister, Anthony Albanese, confirmed that Scott Rush, Matthew Norman, Si-Yi Chen, Martin Stephens and Michael Czugaj returned to Australia from Indonesia on Sunday afternoon.

Having served almost 20 years in jail in Indonesia, the men have had the rest of their life sentences commuted on humanitarian grounds on the condition that they continue rehabilitation in Australia. They are now free but are banned from returning to Indonesia. There was no diplomatic quid pro quo, Guardian Australia understands.

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In a statement released on behalf of the men and their families, the group said they were “immensely grateful” to Indonesia’s president, Prabowo Subianto, and his government as well as successive foreign ministers in Australia who had advocated for their release

“A special mention should be made of the Department of Foreign Affairs and Trade, Dfat,” the statement continued. “In both Australia and Indonesia, at both a senior level and in prison visits and personal assistance, over many years, Dfat have offered professional and enduring support.

“The men and their families will always be grateful. The men and their families thank all those who have assisted them to reach this point. In particular, they thank their Indonesian lawyers, friends in Indonesia, academics and others in Australia, and numerous friends in Australia. This support has been essential and invaluable.”

The statement said that the five men were “relieved and happy” to be back in Australia and that they looked forward to “reintegrating back into and contributing to society”.

In a statement, Albanese said the government “would like to convey our deep appreciation to the government of Indonesia for its cooperation to facilitate the men’s return to Australia on humanitarian grounds,” adding his thanks to the president, Prabowo Subianto, for his “act of compassion”.

“This reflects the strong bilateral relationship and mutual respect between Indonesia and Australia. These Australians served more than 19 years in prison in Indonesia. It was time for them to come home.

“They will now have the opportunity to continue their rehabilitation and reintegration here in Australia.”

The Bali Nine were charged and convicted with trying to smuggle 8.3kg of heroin out of Indonesia in April 2005.

The ringleaders of the drug-smuggling operation, Myuran Sukumaran and Andrew Chan, were sentenced to death and executed by firing squad in Indonesia in 2015. Another member, Tan Duc Than Nguyen, died of cancer in 2018.

The only female member of the group, Renae Lawrence, had her sentence commuted in 2018 and was returned to Australia.

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Albanese said on Sunday that Australia shared Indonesia’s concern about “the serious problem illicit drugs represents” and the two nations would continue to work together to combat it.

Guardian Australia has been told the federal government would provide short-term accommodation for the five men who returned on Sunday. They would have access to medical and other support.

Their life sentences were effectively converted to 20 years, meaning they are considered to have been completed. The Australian government hopes the agreement with Indonesia might serve as a model for future cases.

Australia’s home affairs minister, Tony Burke, signed a ministerial agreement with his Indonesian counterpart to seal the arrangement, which was not a prisoner transfer because the countries’ respective legal systems did not allow for that. The deal was signed after to Burke’s visit to Indonesia this month.

Australian government officials declined to provide details of the men’s location for privacy reasons. They are understood to have returned by commercial aircraft, accompanied by Australian consular officials, and have undertaken voluntarily to continue a rehabilitation program – the details of which were unavailable.

The Australian government consistently raised the case of the Bali Nine with Indonesia. In November Albanese discussed it with Subianto on the sidelines of the Apec summit in Lima.

Since then there has been speculation that an agreement was imminent that would return the five men to Australia.