The Cairo court said Greste, along with Canadian Mohamed Fahmy and Egyptian producer Baher Mohamed, had broadcast "false" news that had harmed Egypt and sentenced them to three years in jail.
The case has become an embarrassment for Egyptian President Abdel Fattah El-Sisi, who has said he wished the reporters had been deported rather than put on trial.
He may pardon them if he chooses.
"In the absence of any evidence of wrongdoing, the only conclusion that we can come to is that this verdict was politically motivated," Greste, who was tried in absentia after being deported early this year, told reporters in Sydney Sunday.
"President Sisi now has an opportunity to undo that injustice, to correct that injustice. The eyes of the world are on Egypt.
"It is now up to President Sisi to do what he said he would do from the outset and that is pardon us if we were ever convicted."
The three journalists were sentenced to between seven and 10 years in jail last year, but an appeals court in January granted them a retrial, saying the verdict had not been backed by evidence.
They were arrested in December 2013, months after the ouster of Islamist president Mohamed Morsi in June of hat year, which was followed by months of political turmoil.
Fahmy and Mohamed were in the Cairo court for the verdict, and Fahmy's lawyer Amal Clooney told reporters she would press the presidency for a pardon.
"It's a dangerous precedent in Egypt that journalists can be locked up simply for reporting the news and courts can be used as political tools," she said.
Canada called for the "immediate return" of Fahmy, while Qatar-based Al-Jazeera denounced the verdict as an "attack on press freedom".
"It's a dark day for the Egyptian judiciary," Giles Trendle, the English channel's acting managing director, told reporters in Doha.
"Rather than defend liberty and the free and fair media, the Egyptian judiciary has compromised its own independence."
Al-Jazeera's head of litigation, Farah Muftah, said in Doha the ruling would be appealed once the judge publishes the basis for his sentencings.
Several co-defendants, accused of working with Al-Jazeera, received similar sentences.
Relatives and supporters were dismayed after the ruling Saturday.
"I'm shocked. Terribly shocked. We waited for an acquittal and then found ourselves stuck again in the case. This is illogical," Fahmy's brother Adel said.
On Saturday, Greste described the jail terms as "devastating".
"We did nothing wrong. The prosecution presented no evidence that we did anything wrong and so for us to be convicted as terrorists on no evidence at all is frankly outrageous," he said.
Judge Hassan Farid said Saturday that it was clear the reporters "were not journalists" and had broadcast "false news" while operating without a permit.
Mohamed received an additional six-month sentence for possessing a bullet he picked up while covering protest violence.
Fahmy and Mohamed, who were released on bail in February at the start of the retrial, were taken into custody.
Lynne Yelich, Canadian minister of state for foreign and consular affairs, called on Egypt "to use all tools at its disposal to resolve Mr Fahmy's case and allow his immediate return to Canada".
Australian Foreign Minister Julie Bishop said she was "dismayed" by the outcome and the United States said it was "deeply disappointed and concerned".
"We urge the government of Egypt to take all available measures to redress this verdict, which undermines the very freedom of expression necessary for stability and development," State Department spokesman John Kirby said in a statement.
British Ministerfor Middle East and North Africa Tobias Ellwood said the sentencings would "undermine confidence in Egypt's progress towards strong long-term stability based on implementing the rights granted by the Egyptian constitution".
A European Union statement called Saturday's sentences a "setback for freedom of expression in Egypt".
Fahmy, who gave up his Egyptian citizenship in hopes of being deported as Greste was in February said ahead of the verdict that the trial was "politicised".
"If justice is to be served we should be acquitted as impartial journalists," said Fahmy, who formerly worked for CNN.
The three were accused of having supported the Brotherhood in their coverage. However, during the trial, the prosecution failed to find fault in their reporting.
"The technical committee that was appointed by the judge gave the court a report stating that none of our reports were fabricated," Fahmy said.
Al-Jazeera's Arabic channel had been supportive of Morsi and Islamists, but Fahmy, Greste and Mohamed worked for its English-language news channel.
Fahmy said they were "shocked" to discover during their trial that the broadcaster was unlicensed, when a prosecutor presented evidence to that effect.
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This story from AFP was edited by Ahram Online.http://english.ahram.org.eg/News/139224.aspx