Greste, 49, was to have a private family reunion after disembarking from his flight before walking out to meet supporters and give a brief statement to the media, a family spokeswoman said.
The award-winning correspondent was on Sunday deported to Cyprus from Cairo, where he was being held for allegedly aiding the blacklisted Muslim Brotherhood.
A group of supporters greeted him at the airport with signs saying 'Welcome Home Peter' and 'Journalism is not a crime' after his plane landed today.
He was charged with aiding the blacklisted Muslim Brotherhood movement, along with Al-Jazeera television colleagues Canadian-Egyptian Mohamed Fahmy and Baher Mohamed of Egypt.
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Both of Greste's colleagues remain in an Egyptian prison, although Fahmy's family said Tuesday he had renounced his Egyptian citizenship hoping to pave the way for his release.
"Special thanks to all who've supported us over the past year. MUST NOT FORGET THOSE STILL IN PRISON," the Australian reporter wrote in a tweet.
He also posted a picture of himself standing in the sea, giving the victory sign, writing: "Free in Cyprus! Feels sweet. Peter back online for first time in 400+ days."
A statement from the prime minister's office said Abbott had "expressed hope that Mr. Greste's colleagues Mohamed Fahmy and Baher Mohamed might be released soon".
Greste was due to hold a press conference later today with his mother Lois, father Juris and brothers Andrew and Mike.