The girls were exchanged for four Boko Haram militants in Banki, northeast Nigeria, said the local sources.
The Nigerian presidency said in a statement that the girls were released after negotiations between Boko Haram, the International Committee of the Red Cross (ICRC) and the Nigerian and Swiss governments.
The statement added that negotiations are ongoing, raising the prospect of more releases."It is confirmed that 21 of the missing Chibok girls have been released and are in the custody of the department of state services," presidential spokesman Garba Shehu said in the statement."The release of the girls... is an outcome of negotiations between the administration and the Boko Haram brokered by the International Red Cross and the Swiss government," Shehu said.
"The negotiations will continue."
"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 taken by helicopter to Maiduguri, the capital of northeast Borno state.
"The 21 (Chibok) girls arrived (in) Banki around 3:00 am (0200 GMT) where they found a military helicopter waiting. They were immediately ushered into the helicopter and flown to Maiduguri," said another local source.
- 'End of the insurgency' -
Over 200 girls were captured from the northeast Nigeria town of Chibok in April 2014 by Boko Haram militants as part of their fight to establish an Islamist state in the region.The audacious kidnapping drew global attention to the jihadist insurgency engulfing the area.Out of the 276 girls kidnapped, scores escaped in the hours after the kidnapping, while another was rescued earlier this year.
In September, the Nigerian government said that it had opened negotiations with Boko Haram to secure the release of the remaining girls but that the talks were derailed due to a split in the extremist group.
The identity of the girls has yet to be confirmed, said Bring Back Our Girls campaigner Aisha Yesufu."We cannot confirm anything yet," Yesufu said.
"As I depart Abuja for Germany on an official visit, I welcome the release of 21 of our Chibok girls, following successful negotiations," Nigerian President Muhammadu Buhari said in a statement on Twitter.
Prisoner swaps between Boko Haram and the Nigerian government have happened before, said Ryan Cummings, director at intelligence firm Signal Risk.
"Obviously the guys that Boko Haram wants released would be more high ranking," Cummings said.
"The trajectory of the insurgency has shifted in the favour of the Nigerian government of late."Let's hope that it's the start to negotiations to find the end of the insurgency."
The insurgency has claimed more than 20,000 lives, displaced 2.6 million people from their homes and thousands of children have been kidnapped since Boko Haram took up arms against the Nigerian government in 2009.