Bergdahl, the only US soldier captured by the Taliban since the war began in 2001, was freed in exchange for five senior insurgent detainees as both parties claimed success for the dramatic deal, brokered by Qatar.
But the swap was criticised by several Republican lawmakers who demanded to know whether the Taliban prisoners would return to fighting the United States.
In an interview with NBC's "Meet the Press," Hagel staunchly defended the trade as an effort to save Bergdahl's life and said it could provide a breakthrough for peace in Afghanistan.
"So maybe this will be a new opening that can produce an agreement," he said, noting that the United States had engaged in talks with the Taliban in the past.
Mullah Mohammad Omar, the spiritual leader of the Taliban, also issued a rare statement praising the "big victory" for the Afghan Muslim nation in a sign seen by a government negotiator and some analysts as potential confidence building measure.
Earlier on Sunday, Hagel paid a brief unannounced visit to Bagram air base north of Kabul, where he met privately with more than a dozen of the team that carried out the exchange mission, according to the Washington Post.
"We believed that the information that we had, the intelligence that we had, was such that Sgt. Bergdahl's safety and health were both in jeopardy and, in particular, his health was deteriorating," he told US media.
"It was our judgment that if we could find an opening and move very quickly... that we could get him out of there, essentially to save his life," he added.
Bergdahl's release came four days after President Barack Obama announced a timetable for a final US pullout by end-2016.
The five Guantanamo prisoners were named as Mohammad Fazl, Norullah Noori, Mohammed Nabi, Khairullah Khairkhwa and Abdul Haq Wasiq, all influential former officials of the Taliban regime toppled by the US-led invasion of Afghanistan after the 9/11 attacks.
They were swapped for Idaho native Bergdahl, who disappeared from a base in Afghanistan's eastern Paktika province.
A senior US administration official confirmed that the United States had transferred the five Afghan Guantanamo detainees to Qatar, as did a Taliban statement which added the men were with their families.
A separate source said the Taliban detainees would spend the year in Qatar.
'This will help peace'
"I think it shows all sides' goodwill for trust-building and start of the peace talks in near future," Ismail Qasimyar, of Afghanistan's High Peace Council, said of the deal.
Borhan Osman, a researcher and analyst said the deal, while not directly connected to the peace process, could increase both sides' confidence in each other.
"It does bolster the Taliban's political office's status as sort of reliable address for the movement," he said, referring to the group's "embassy" in Qatar.
"The trade of prisoners in a smooth manner would naturally serve as a 'nice' measure, that could be followed by more measures towards peace talks if they want to," he added.
The men's release had long been the main condition imposed by the Taliban to launch peace negotiations with the United States.
Obama appeared with Bergdahl's parents at the White House to announce his release.
"Today the American people are pleased that we will be able to welcome home Sergeant Bowe Bergdahl, held captive for nearly five years," he said.
Obama also expressed his "deepest appreciation" to the Emir of Qatar for his help in securing the return.
Bergdahl was in good condition after the Taliban handed him over to "a few dozen" US special forces backed up by helicopters at an undisclosed location in eastern Afghanistan, defence officials said.
According to officials quoted in US media he appeared to have difficult speaking English after five-years with Pashto speaking Afghans.
Pentagon officials said he was brought to Bagram for medical treatment, and was then flown to the US military medical facility at Landstuhl in Germany for further treatment and evaluation.
He will later be flown back home to be reunited with his family.
Since his capture, Bergdahl has appeared in several Taliban videos.
In January the United States obtained a "proof of life" video of the soldier -- the first concrete evidence in more than three years that he was still alive.
In his statement, Obama said "Sergeant Bergdahl's recovery is a reminder of America's unwavering commitment to leave no man or woman in uniform behind on the battlefield."
Several of his Republican opponents took a harsher view of the deal.
Influential Senator John McCain demanded to know what steps were being taken to "ensure that these vicious and violent Taliban extremists never return to fight against the United States and our partners."
McCain described the men being released as "hardened terrorists who have the blood of Americans and countless Afghans on their hands".