Local sources said their release was part of a prisoner swap with the Nigerian government, but the authorities denied doing a deal with Boko Haram.
Declaring Thursday's release "significant", Nigerian officials said the breakthrough would help the recovery of the 197 girls who remain in captivity.
"It's just a first step in what we believe will lead to the eventual release of all our girls," Nigerian information minister Lai Mohammed said in Abuja.
"When you are fighting an insurgency, it's a combination of carrot and stick," Mohammed said. "The release of these girls does not mean the end to military operations. But it could mean a new phase in the conduct of the war against terror."
In a statement, the Nigerian presidency said the girls were freed after negotiations between Boko Haram and the Nigerian government brokered by the International Committee of the Red Cross (ICRC) and the Swiss government.
Some of the freed Chibok school girls are seen at the state House in Abuja, Nigeria, Thursday, Oct. 13, 2016 (AAP) Source: AAP
"Switzerland facilitated contacts between representatives of the Nigerian government and intermediaries of Boko Haram on the release of the Chibok girls," confirmed Swiss foreign ministry spokesman Pierre-Alain Eltschinger.
The girls were exchanged for four Boko Haram militants in Banki, a town in northeast Nigeria close to the Cameroon border, said local sources.
"The girls were brought to Kumshe, which is 15 kilometres (nine miles) from Banki where a military base is stationed, in ICRC vehicles," said a local source.
"The four Boko Haram militants were brought to Banki from Maiduguri in a military helicopter from where they were driven to Kumshe in ICRC vehicles."
From Kumshe the Chibok girls were flown by helicopter to Maiduguri, capital of northeast Borno state, said another local source.
Nigeria Vice President ,Yemi Osinbajo, left, receives some of the freed Chibok school girls at the state House in Abuja, Nigeria, Thursday, Oct. 13, 2016 (AAP) Source: AP
'Not a swap'
Information minister Mohammed denied that the 21 girls were exchanged for Boko Haram prisoners, saying "this is not a swap."
"It is a release, the product of painstaking negotiations and trust on both sides," he added.
In September, the Nigerian government had admitted it had come close to a swap last year, but that talks broke down.
The Chibok girls were abducted in April 2014, drawing global attention to the Boko Haram insurgency engulfing the area when US First Lady Michelle Obama joined the #BringBackOurGirls online movement.
Of the 276 girls initially seized, scores escaped in the hours after the kidnapping, while another 19-year-old was found with her four-month-old baby earlier this year.
Despite winning back swathes of territory from the jihadists, Nigerian President Muhammadu Buhari had faced intense criticism for failing to recover the young captives girls, who became the defining symbol of Boko Haram's brutal campaign to establish a fundamentalist Islamic state in the country.
The identity of the girls freed on Thursday has yet to be confirmed, said Bring Back Our Girls campaigner Aisha Yesufu."We cannot confirm anything yet," she said.
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'Stepping stone'
The alleged swap was "bittersweet" said Ryan Cummings, director at intelligence firm Signal Risk.
"Whatever is being given to Boko Haram in exchange for the girls would potentially be used against the Nigerian state again."
While the return of the 21 girls is an encouraging sign, analysts point out that Boko Haram is still a potent force in the region with rival factions competing for control.
"It's a good stepping stone and a good process but I think we should keep our expectations a bit realistic," Omar Mahmood, a researcher at the Pretoria-based Institute for Security Studies.
"They are still very capable of conducting attacks, we've seen that in Maiduguri."
On Wednesday, Boko Haram was believed to be behind a suicide attack that saw eight people killed in Maiduguri.
The insurgency has claimed more than 20,000 lives and displaced 2.6 million people from their homes since Boko Haram took up arms against the Nigerian government in 2009.
