Cairo deported the award-winning correspondent for Al-Jazeera English television yesterday after more than 400 days in detention on charges of backing the Muslim Brotherhood.
"I'm ecstatic," his mother Lois told a press conference in their hometown Brisbane.
"I just can't say how happy I am about it."
The reporter was detained along with two colleagues, Canadian-Egyptian Mohamed Fahmy and an Egyptian producer, Baher Mohamed, in December 2013 and charged with aiding the blacklisted Brotherhood.
"He is gathering his thoughts for the trip home," brother Andrew said.
"He is safe, healthy, very, very happy to be on his way home."
The family had spoken to Greste several times and stressed the importance of his colleagues being released too.
"He's not going to forget his two other colleagues," Andrew said.
"There's no doubt that his excitement is tempered and restrained and will be until those guys are free, he won't give up until Baher and Mohamed Fahmy are out of there."
The family of their Egyptian colleague Baher Mohamed have pinned their hopes for his release on a presidential pardon or his acquittal on appeal.
The Greste family said Peter had yet to come to terms with his sudden release.
"He was in a state of being -- finding it difficult to believe," his mother said.
"He's totally -- he said it all happened so fast and so quick, he's still absorbing it all and I think it's going to take him several days."
The Greste family paid tribute to "all the people who have supported him who have given time, money, and energy in seeking his freedom.
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