The five remaining members of the infamous "Bali Nine" drug ring say they are "relieved and happy" to be home in Australia, after spending nearly 20 years in Indonesian prisons.

Matthew Norman, Scott Rush, Martin Stephens, Si Yi Chen, and Michael Czugaj arrived in Darwin on Sunday after years of lobbying with Australia on their behalf.

"They look forward, in time, to reintegrating into society and contributing," said a statement issued on behalf of the men and their families.

The high-profile case began in 2005 when Indonesia caught nine young Australians trying to smuggle 8.3kg (18lb) of heroin out of Bali attached to their bodies.

The eight men and one woman were arrested at an airport and hotel in Bali following a tip from Australian police.

The case made global headlines when two of the group's leaders, Andrew Chan and Myuran Sukumaran, were executed by firing squad in 2015 - sparking a diplomatic row between neighbors Indonesia and Australia.

Other members of the Bali Nine - most of them under the age of 21 - were sentenced to 20 years or life in prison.

The case highlighted Indonesia's strict drug laws, some of the toughest in the world.

One of the nine, Tan Duc Thanh Nguyen, died of cancer in prison in 2018. Soon after, Renae Lawrence, then 41, the only woman among the group, commuted her sentence after nearly spent 13 years in prison and returned to Australia. one year

Indonesia did not serve the sentences of the remaining five, who are now between 38 and 48, and they were transported back to Australia as prisoners. But the Australian Broadcasting Corporation (ABC) has reported that the men are effectively free to live unhindered in Australian society.

The five have been banned for life from entering Indonesia, a government spokesman said in a statement.

On Monday, Australian Prime Minister Anthony Albanese said he had spoken to several of the men's "grateful" parents.

"They committed a serious crime and they have rightly paid a heavy price for it. But it was time for them to come home," he told reporters.

He said the agreement did not come with conditions or favors that Australia had to pay back: "This is an act of sympathy by President Prabowo (Subianto) and we give thank him for it."

The men and their families also said they were "extremely grateful" to Prabowo.

They also thanked the lawyers, diplomats and government figures who helped advocate for them over the past two decades, before requesting privacy.

"The welfare of the men is a priority, they will need time and support, and we hope and hope that the media and our community will contribute to this."

The five men are being put through medical checks at Darwin's Howard Springs facility - which was used for quarantine during the pandemic - and will begin a voluntary "rehabilitation process", the Education Minister said Jason Clare. It is not clear what that means, or how long the men will stay there.

He said normal visa processes would apply to Indonesian family members of the men, who did not follow them to Australia.

The Bishop of Townsville, Timothy Harris, who has supported the families of Scott Rush and Michael Czugaj since their arrest, said he immediately called Scott Rush's father Lee when he heard the news.

Scott's parents are eagerly awaiting the meeting, Bishop Harris told the BBC.

"They are ashamed of what their son has done. They always believed he had committed a crime... But this turn of events is filled with a sense of anticipation."

However, he said it would take time for the men to heal from their experience and reintegrate into society.

"If you think your son is committing a crime (and has been) imprisoned in a foreign country, they come back. How can someone rejoin the family, let alone the society?"

"Things have changed. The relationships have to be reconnected. They have to face that as time goes on," he said.

"Once (Scott's family) gets a hold of him ... I hope and pray that things will be better, because there's nothing like your family (close by)."