The Greste family spent 400 days fighting for their son's freedom. In the end it came so fast it made their heads spin.

But exactly when the Al Jazeera journalist will be back on Australian soil remains unclear, as his family closes ranks around him to protect his mental health.

They say he'll need time in his safe haven of Cyprus, to digest the fact he's finally free after more than a year in an Egyptian jail.

He was jailed after being accused of spreading false news and supporting the banned Islamist movement of deposed president Mohamed Morsi.

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His euphoric family have spoken of their guarded hope when the rumour mill went into overdrive at the weekend, with their sources in Egypt and in Australia telling them Peter could soon walk free.

Within hours it had happened, and by early on Monday, Australian time, he was in Cyprus, with his brother Michael by his side.

Australian diplomats on the ground in Cairo, who had worked so tirelessly for Peter's freedom, whisked him straight from prison and onto a plane bound for the safety of the Mediterranean island country.

And that's where he'll stay for as long as he needs to.

"I think he'll recover well but he needs that space," his ecstatic mother Lois Greste told reporters on Monday.

"(He'll come back) when he's ready to come back. And not before."

Lois, father Juris, and brother Andrew laughed and at times blinked back tears as they spoke of the extraordinary international campaign to free Peter and two of his Al Jazeera colleagues following their arrest in December 2013.

They said Peter wanted to thank everyday Australians, journalists world wide, and leaders including US President Barack Obama and Prime Minister Tony Abbott for fighting to free him from his seven-year jail term.

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There was special thanks too for Foreign Minister Julie Bishop, but the highest praise was reserved for diplomats, particularly those on the ground in Cairo, who did the leg work.

"While we're in knighthood mode, I would commend them and recommend them for a collective knighthood, one and all," Juris told reporters.

The family's euphoria has been tempered by the fact Peter's colleagues - Canadian-Egyptian Mohamed Fahmy and producer Baher Mohamed, who is Egyptian - remain locked up on charges described as politically motivated.

"They also deserve to be freed. We hope your struggle will end very soon," brother Andrew said.

Fahmy's relatives expect him to taste freedom soon under the same law that allowed Mr Greste's deportation. But their Egyptian colleague Mohamed does not have a foreign passport. His family is hoping for a presidential pardon, or his acquittal on appeal.

Mr Abbott said the role of Morsi's successor could not be underestimated, and he was delighted Abdel Fattah al-Sisi had ordered Greste's expulsion under a new law permitting foreign prisoners to be deported.

He also paid tribute to Ms Bishop and to the Greste family's unwavering determination.

"You never gave up hope and your strength is an inspiration to all of us," Mr Abbott said.

When Peter Greste finally returns to Brisbane in the coming days or weeks it will be into the arms of an emotional family who will want to keep him close.

And to a meal of beer and prawns.

"There'll be a tear or two shed, I think," brother Andrew said.

"And mum will probably put him over her knee," his father added.

- AAP