Joshua Boyle, a Canadian, boarded a flight in Islamabad with his American wife Caitlan Coleman and their three children, the Pakistani military source told CNN. They will fly on to Canada from London.
An Inter-Services Public Relations (ISPR) statement said the hostages were rescued on Thursday "through an intelligence-based operation by Pakistani troops and the Inter-Services Intelligence (ISI)". The Army said it acted on intelligence shared by the US.
Boyle and Coleman were held for five years by the Taliban-affiliated Haqqani network in Afghanistan.
Their three children were born during their time in captivity.
"US intelligence agencies had been tracking them and shared their shifting across to Pakistan on October 11, 2017, through the Kurram Agency border," the ISPR said.
A US military official said a hostage team had flown to Pakistan to fly the family out but Boyle refused to board an American military plane over concerns he could face arrest.
Boyle was previously married to Zaynab Khadr, a sister of Canadian-born Guantánamo Bay detainee Omar Khadr and the daughter of a senior Al Qaeda financier. According to reports, her father and the family stayed with Osama bin Laden for sometime.
The US official said there were some questions surrounding Boyle's past but the Department of Justice said he did not face arrest.
"Coleman and Boyle are not charged with any federal crime and as such we do not seek their arrest," spokesman Wyn Hornbuckle said.
Boyle's father, Patrick, told CNN that his son had described the rescue mission during a phone call.
"The five of them being in the back of a car being transferred and a car being stopped, surrounded by, Josh described, 35 Pakistani Army officials," Patrick Boyle said.
"A firefight breaking out, that all five captors had been killed by the Pakistani Army, and all five of our Boyles were safe and okay. Josh... was hit with some shrapnel and our governments confirmed that he was damaged in the leg. That's all we know right now about that."
Patrick Boyle said the sudden turn of events was nothing short of miraculous.
"Cait (Caitlan), in her last video said if all five of them make it out, it's going to be a miracle," he said. "And we're living a miracle."
US President Donald Trump applauded the development and said that the release was "a positive moment" for the Washington-Islamabad relationship.
He also praised Pakistan's cooperation, saying it was "a sign that it is honouring America's wishes for it to do more to provide security in the region".
Canadian Prime Minister Justin Trudeau also expressed "his gratitude to his nation's allies for their help in rescuing a native family from the Taliban who held them hostage since 2012".
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