Foreign Minister John Baird told Canada's public broadcaster that the release of the Egyptian-Canadian was "imminent", in a statement his spokesman confirmed but declined to elaborate on.
The news came as Canadian diplomats reportedly met with their counterparts in Cairo to press for the release of the dual national.
Fahmy was arrested for allegedly aiding the blacklisted Muslim Brotherhood along with Greste and Egyptian producer Baher Mohamed, in moves that sparked worldwide condemnation.
Greste expressed hope that Egypt would release his colleagues, in an interview with the pan-Arab network a day after he was freed and flew to Cyprus where he has been resting before returning to Australia.
"This is a massive step forward... I just hope that Egypt keeps going down this path with the others," said the 49-year-old Australian.
Greste said he felt a "real mix of emotions boiling inside" upon hearing the unexpected news that he was to be released because it meant leaving behind "my brothers" Fahmy and Mohamed.
"I feel incredible angst about my colleagues, leaving them behind," he said.
"Amidst all this relief, I still feel a sense of concern. If it's appropriate for me to be free, it's right for all of them to be freed."
Greste said he was overwhelmed by the level of support for the campaign for his release, and that he now looked forward to "watching a few sunsets" and "feeling sand under my toes".
"This has been like a rebirth and you realise that it is those little beautiful moments in life... that's what's important."
Fahmy's relatives have said they expect him to be deported under a decree passed by Egypt's President Abdel Fattah al-Sisi that allows for the transfer of foreigners on trial.
His fiancee, Marwa Omara, told AFP in Cairo: "We are expecting Mohamed to be released in the coming days."
Greste's family expressed their joy after speaking to him on the phone.
The Australian's mother, Lois, told a news conference in their hometown of Brisbane: "I'm ecstatic. I just can't say how happy I am about it."
His father Juris said it was not clear when he would arrive home.
"He is gathering his thoughts for the trip home," said his brother Andrew. "He is safe, healthy, very, very happy to be on his way home."
Australian Prime Minister Tony Abbott spoke of his "personal delight and our nation's relief" at Greste's release.
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He also voiced support for a free media and thanked Sisi.
Al-Jazeera vowed to pursue the campaign to free the other two journalists.
But Heather Allan, head of newsgathering at the channel, admitted she wasn't confident that Mohamed would be released.
"I can't say I am confident, no. I just don't know, honestly. Are we going to keep on fighting it? Absolutely -- we are not going to leave him there," she said.
Mohamed's family has pinned their hopes on a presidential pardon or his acquittal on appeal.
Amnesty International said Greste's release should not overshadow the ongoing imprisonment of Fahmy and Mohamed.
"All three men are facing trumped up charges and were forced to endure a farcical trial marred by irregularities," said Amnesty's Hassiba Hadj Sahraoui.
The United States joined the United Nations and European Union in welcoming Greste's release.
US State Department spokeswoman Jen Psaki also urged the Egyptian government to take "measures to address the verdicts against detained journalists and peaceful civil society activists".
Nightmare for Sisi
The high-profile trial, at which Greste and Fahmy were sentenced to seven years in prison and Mohamed to 10, proved a public relations nightmare for Sisi, who has cracked down on Islamists since toppling president Mohamed Morsi in July 2013.
The verdict was overturned and a court in January ordered a retrial for the three.
Egyptian police arrested the journalists at the peak of a diplomatic row between Cairo and Qatar, which owns Al-Jazeera.
The broadcaster had been critical of the deadly crackdown on Morsi's Muslim Brotherhood following the Islamist leader's overthrow.
Qatar has since moved to mend ties with Egypt, and Al-Jazeera has closed its Arabic-language Egyptian affiliate which backed the Brotherhood.
The rapprochement reflected growing international acceptance of the crackdown on Egypt's Islamist opposition and militants who have killed scores of police and soldiers since Morsi's overthrow.
The crackdown, which has left at least 1,400 people dead, had tested Egypt's ties with the United States, which temporarily froze part of its annual $1.3 billion military aid in 2013.
Greste worked for multiple news organisations before joining Al-Jazeera English.
He was the BBC's Kabul correspondent in 1995 and returned there after the US-led invasion in 2001.
From 2009, he was based in Nairobi, winning the broadcasting industry's prestigious Peabody Award in 2011.