The White House has welcomed the release of Australian man Timothy Weeks and his US colleague Kevin King after more than three years as hostages of the Taliban.

Key points: Mr Weeks and Mr King had been held hostage since 2016

Mr Weeks and Mr King had been held hostage since 2016 The two were teaching in Kabul when they were abducted

The two were teaching in Kabul when they were abducted The younger brother of the Taliban's deputy leader is believed to be part of the prisoner swap

In a release Tuesday morning (local time), the White House said the men, professors at the American University of Afghanistan when they were kidnapped at gunpoint in August 2016, were currently receiving medical care and other support from the US Government.

"We pray for the full recovery of both men, who endured significant hardship during their captivity, and wish them well as they reunite with their loved ones in the near future," the statement read.

"We thank the Afghan government for its actions, in the spirit of our partnership that enabled the freeing of the hostages.

"The Trump Administration will continue to work to ensure that Afghanistan is never again used to launch terrorist attacks against the United States and our allies."

Earlier, Taliban and Afghan police officials said Mr Weeks and Mr King had been released in Zabul province, in southern Afghanistan, near the Pakistan border.

It is understood the men would be flown from Afghanistan to Germany, where the US military has a large base at Stuttgart, for initial medical checks.

Mr Weeks' father, Mervyn, learned of his son's release after the three-year ordeal via a phone call from the Department of Foreign Affairs and Trade.

"Very relieved. All I want to say at this stage is that I want to thank all those who've supported us and prayed with us for this eventuality," Mervyn Weeks told the ABC.

Mr Weeks said he was yet to speak to his son himself and was unsure whether his son would be returning to Australia.

"I can't say any more because I know what's in place, but I don't know what he would want," Mervyn Weeks added.

Asked if he felt the Australian Government had done enough to press for his son's release, Mervyn Weeks replied "Certainly, yes. They've been very, very good."

Mr Weeks and Mr King were abducted in 2016 outside the American University in Kabul where they both worked as teachers.

The following year, the Taliban released two videos showing the captives. A January 2017 video showed them appearing pale and gaunt. In the later video, Mr King and Mr Weeks looked healthier and said a deadline for their release was set for June 16 that year.

In that video, Mr Weeks pleaded with then-Australian prime minister Malcolm Turnbull to negotiate his release.

Scott Morrison responds

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 45 seconds 45 s Scott Morrison thanks the Afghan Government, US President Donald Trump and Secretary Mike Pompeo.

Prime Minister Scott Morrison thanked the governments involved in the release at a press conference on Wednesday.

He tweeted his response late on Tuesday night and said Mr Weeks' family had asked for privacy.

"We are profoundly pleased and relieved Australian Tim Weeks & his US colleague, Kevin King, who were held hostage since August 2016, have been released by their kidnappers today in Afghanistan," he wrote.

"We convey deep appreciation to the Governments of the United States & Afghanistan.

"Tim's family has asked for privacy. They have asked the Australian Government to convey their relief that their long ordeal is over, and their gratitude to all those who have contributed to Tim's safe return."

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Their release on Tuesday came as part of a prisoner swap deal which saw three Taliban prisoners released by the Kabul government and flown to Qatar.

The three included Anas Haqqani, the younger brother of the Taliban's deputy, Sirajuddin Haqqani, who also heads the fearsome Haqqani network.

Afghan President Ashraf Ghani last week announced the "conditional release" of the Taliban figures, saying at a press event broadcast live on state television that it was a very hard decision he felt he had to make in the interest of the Afghan people.

The American University in Kabul released a statement expressing its happiness that the pair had been released.

"AUAF welcomes the news of the release of our colleagues, Kevin King and Timothy Weeks, who had been held hostage since August 7, 2016," the statement read.

"The AUAF community shares the relief of the families of Kevin and Timothy, and we look forward to providing all the support we can to Kevin and Tim and their families. We wish to extend our gratitude to all involved in the release of our colleagues.

"The AUAF community, our students, faculty and staff, have keenly felt the absence of our two colleagues even as we have continually urged their release over these past three years."

Afghan security personnel escort arrested alleged Taliban and Islamic State militants during an operation. ( AFP: Noorullah Shirzada )

United States Secretary of State Mike Pompeo and National Security Adviser Robert O'Brien made separate calls to Mr Ghani on Monday to discuss the prisoners; release, Mr Ghani's spokesman Sediq Sediqqi said.

The swap was intended to try to restart talks to end Afghanistan's 18-year war and allow for the eventual withdrawal of US troops from Afghanistan.

The United States had been close to an agreement in September with the Taliban but a fresh wave of violence in the Afghan capital that killed a US soldier brought the impending deal to a grinding halt.