Greste, an award-winning correspondent for Al-Jazeera English television, flew to Cyprus with brother Michael after his release from Cairo's Tora prison yesterday, Egyptian officials told AFP.
Greste was detained with colleagues Canadian-Egyptian Mohamed Fahmy and Egyptian producer Baher Mohamed in December 2013 for allegedly aiding the blacklisted Brotherhood.
Their arrest sparked worldwide condemnation, with Washington and the United Nations leading calls for their release.
His fiancee, Marwa Omara, told AFP in Cairo: "We are expecting Mohamed to be released in the coming days."
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Canada said Greste's release was "positive" and that it remained "very hopeful" that Fahmy would also be freed soon.
Greste's family expressed their joy after speaking to Peter on the phone and vowed his colleagues still behind bars would not be forgotten.
"He's not going to forget his two other colleagues," Peter's brother Andrew said after the pair spoke on the telephone.
Andrew added: "There's no doubt that his excitement is tempered and restrained and will be until those guys are free."
The Australian's mother, Lois, told a press conference in their hometown of Brisbane: "I'm ecstatic. I just can't say how happy I am about it."
Greste was resting in Cyprus, and father Juris said it was not clear when he would arrive home.
"He is gathering his thoughts for the trip home," said Andrew. "He is safe, healthy, very, very happy to be on his way home."