Gen. David Hurley, Australia's military chief, confirmed in a written statement the extradition of the former soldier, identified as Sgt. Hekmatullah, happened Tuesday, saying the ISI had arrested him in February.
Hekmatullah is expected to face trial for the murder of Lance Cpl. Rick Milosevic, Sapper James Martin and Pvt. Robert Poate at Patrol Base Wahab in Afghanistan in August 2012.
If found guilty, he could face a death sentence.
The three Australian soldiers -- called diggers -- were killed and two others were wounded along with several Afghans during the insider attack, called a green-on-blue attack.
They were machine-gunned while relaxing in the evening at their base.
"We have been relentless and determined in our efforts to pursue those who have murdered and wounded our people," Hurley said.
"We will continue to cooperate with Afghan authorities as they prosecute the case for justice for these Australians."
A statement by the Australian Ministry of Defense said Australia was notified formally of Hekmatullah's capture in February after he was tracked down using cellphone data.
Since then, the Pakistani government, the Afghan National Directorate of Security and Afghanistan's Ministry of Foreign Affairs have been working to establish an appropriate transfer arrangement to return Hekmatullah to Afghanistan.
"The Australian Secret Intelligence Service and the Defense Intelligence Organization have worked closely with ISI and [Afghanistan's] NDS over the past six months to facilitate Hekmatullah's detention and deportation," Hurley said.
"We greatly appreciate their efforts to date and we will continue to cooperate with Afghan authorities. This news comes at a particularly difficult time for the families so close to the anniversary of the incident," he said.
Hurley said there were events in the region, including an election in Pakistan, that created unavoidable delays in extraditing Hekmatullah.
But his capture and extradition "draws a line under the four insider attacks" on Australian personnel, with all four suspects in the other attacks either dead or captured, Hurley said.
"Those responsible for the deaths of seven Australian soldiers and who wounded another 10 have been captured or killed, and no longer pose a threat to [Australian military] personnel," he said.
The Age newspaper reported Afghanistan's ambassador to Australia, Nasir Ahmad Andisha, saying Afghani courts will deal harshly with Hekmatullah if he is found guilty.
"[The Australians] were there to support the people and the government of Afghanistan, so we have no doubt that this Sgt. Hekmatullah will get the maximum punishment if found guilty under Afghan law," Andisha said.
"We have the death penalty as the maximum punishment."
Hugh Poate, father of Robert Poate, said the extradition is "a giant step forward" for the families, The Age newspaper reported.
He thanked the Australian intelligence officials for working toward extradition in what "must have been very difficult" job, The Age said.
Last month, an Australian government report on the incident found the soldiers failed to take adequate security measures to ensure their own safety.
On the day of the report's release, Australian Broadcasting Corp. aired a television report on the attack in which survivor Sgt. Corey Neill gave a graphic account of the event.
Several soldiers had been bivouacked beside their armored vehicle and had been playing cards just before going to bed.
Hekmatullah crept up to the side of the vehicle and opened fire, twice, at point-blank range, spraying the area with machine-gun fire.
The report found the soldiers had failed to set up a secure area that was separate from the Afghani soldiers' area.
The Australians also had been wearing only gym clothes under body armor -- or no body armor.
Two soldiers were disciplined over the lack of sufficient security measures, ABC reported.
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