Mr Greste’s deportation from Egypt after 400 days in prison has been greeted as a “welcome relief” by human rights campaigners.
The Australian left on an EgyptAir flight to Larnaca, Cyprus, after the president approved his deportation in a case that has drawn international condemnation.
Mr Greste, 49, was arrested in December 2013 and imprisoned last June on charges that included spreading false news. He was jailed with two other al-Jazeera journalists, Mohamed Fahmy and Baher Mohamed.
Speaking at a press conference in Brisbane, his brother Andrew told reporters: “He is very happy to be on his way home.
“On a sombre note, I know Peter wanted me to make this point: Peter’s two other colleagues are still there. They also deserve to be freed. Peter won’t rest until they are released from prison.”
His family, who managed to speak to him on the phone, said he was in “great spirits” and would return to Australia “when he is ready”.
Andrew Greste also thanked everyone who had tweeted to back the campaign, saying: “Without the worldwide support, we could not have got through it.”
Hassiba Hadj Sahraoui, Amnesty International’s Middle East and North Africa deputy director, described Mr Greste’s deportation as “a welcome relief but nothing can make up for his ordeal”.
BBC news and current affairs director James Harding said: “He was jailed for nothing more than doing his job; all our thoughts must now be with his two colleagues in the hope that they too will shortly be freed”.
Mr Greste, Egyptian-Canadian Mr Fahmy and Egyptian Mr Mohamed were sentenced to at least seven years in prison on terrorism-related charges last year in a trial described as a sham by rights groups. There was no immediate word on the other two journalists.
Mr Greste was released following a presidential “approval”, officials said, following a new deportation law passed last year.
Mr Greste and Mr Fahmy had sought deportation under new Egyptian legislation which allows foreign nationals to be transferred to their home countries to face trial or serve their sentences in cases of the “highest interest of the state”.
The convictions of all three men were overturned by the Court of Cassation on 1 January on procedural grounds, but they were kept in detention pending a retrial.
Acting Al-Jazeera director-general Mostefa Souag said the Qatar-based network “will not rest until Baher and Mohamed also regain their freedom”.
The sentiment was echoed by Ms Sahraoui, who added: “It is vital that in the celebratory fanfare surrounding his deportation the world does not forget the continuing ordeal of Baher Mohamed and Mohamed Fahmy, who remain behind bars at Tora prison in Cairo.”