The presidency announced that months of talks with the jihadists had "yielded results", just over six months after 21 of their classmates were freed with the help of international mediators.
"Today 82 more Chibok girls were released," it said.
"After lengthy negotiations, our security agencies have taken back these girls, in exchange for some Boko Haram suspects held by the authorities."
No details were given about how many suspects were released or their identities.
The girls were to be taken to Abuja on Sunday to meet President Muhammadu Buhari, the presidency said, thanking security agencies, the Swiss government and the International Committee of the Red Cross (ICRC).
"The president has repeatedly expressed his total commitment towards ensuring the safe return of the Chibok girls and all other Boko Haram captives," it added.
A military and a civilian militia source in Banki, near the border with Cameroon, said "at least 80" girls were brought to the town late afternoon on Saturday and taken to military barracks.
Shehu Sani, a Nigerian senator who has been involved in previous negotiations with Boko Haram, told AFP the girls were mostly "in good condition".
The talks lasted for "almost three to four months" and had initially discussed the release of 50 girls but the number was later increased, he said.
The government would now look to securing the release of the remaining hostages, he added.
