The bilateral agreement was announced by Indonesian President Susilo Bambang Yudhoyono and Australian Prime Minister Julia Gillard during their annual working meeting in the northern city of Darwin, capital of the Northern Territory.
The two leaders also agreed to move faster on finalizing a mutual extradition treaty, making it easier to repatriate asylum seekers to Indonesia, a report by The Age newspaper said.
Susilo urged Gillard to return another 54 underage asylum boat crew members held in Australia, the report said.
The issue of what to do with asylum seekers has been complicated by the presence of some underage crew members. Their status as willing crew members or enforced laborers can be in question, as well as their exact ages.
Susilo said he welcomed Australia's release of more than 50 underage sailors who had acted as crew on asylum vessels, declaring "they are also victims of acts of people-smuggling."
"No doubt we hope that repatriation of the remaining underage seafarers can be accelerated," he said. "We hope another 54 will be released."
The Age said many of the 79 Indonesian crew members held in Australian detention centers say they are minors, meaning they would not be prosecuted but safely returned to Indonesia.
The Australian government has come in for criticism from Jakarta and Australia's human rights commissioner over prolonged detention of suspected minors arrested for people smuggling.
In May, Australian Foreign Minister Bob Carr said the government has no desire to detain minors if they are involved in any way with people smuggling.
Carr was speaking on the issue at a time government critics claimed the Foreign Ministry was striking a deal with Indonesia to send back three detained minors in exchange for a reduction of five years to the sentence of an Australian woman, Schapelle Corby, 34, originally serving 20 years in Bali, Indonesia, for smuggling marijuana.
"At no stage has the (Australian) government sat down with our Indonesian counterparts and said, 'We'll release minors from our jails if you consider a clemency application by Ms. Corby,'" Carr said.
"But if doing what we're doing for the right reasons on these minors has created a level of comfort in the government in Indonesia then that's fine by me. When it comes to minors it's plainly wrong that you've got these kids collected in people-smuggling operations on boats at the wrong time stuck in adult prisons."
During the meeting with Susilo, Gillard said they discussed the importance of the Bali Process in combating people smuggling.
"I welcome the cooperation we have with Indonesia on people smuggling including Indonesia's law enforcement efforts against people-smuggling syndicates," she said.
Australia's detention centers -- especially the main center on Christmas Island -- are full or near capacity as the country copes with thousands of asylum seekers annually.
Australia's Department of Immigration and Citizenship says by the end of June nearly 5,000 "irregular maritime arrivals" had arrived in Australian waters this year.
Last year, around 6,500 asylum seekers were detained.
To relieve the overcrowding, Gillard's government has proposed opening refugee detention centers in other countries under bilateral agreements.
But the latest such controversial plan -- to reopen a disused center on Nauru, in the South Pacific -- was voted down this month in the upper house, the Senate, although it was passed by the lower house, Parliament.
Nauru, in the South Pacific and at 8 square miles the world's smallest republic, has a population of just more than 9,000. Although independent since 1968, it remains under the protection of Australia.
From 2001-08, Nauru accepted aid from Australia in exchange for setting up a refugee center.
The defeated asylum bill must now go back to Parliament for amendments before being reintroduced into the Senate.
Gillard said passing asylum legislation including the vetoed bill is a matter of life and death.
"I don't want to see a 13-year-old girl drown at sea in the weeks between now and when this Parliament comes back in the spring. I don't want to see that," she told Australian Broadcasting Corp. Radio.