They were handed over in exchange for Boko Haram suspects after negotiations.
The girls arrived in the capital Abuja on Sunday, and will be received by President Muhammadu Buhari.
The abduction of the so-called "Chibok girls" triggered a global outcry and sparked a huge social media campaign.
Before the latest release, about 195 of the girls were still missing.
The number of Boko Haram suspects released by authorities remains undisclosed.
The 82 schoolgirls are now in the custody of the Nigerian army and were brought by road convoy from a remote area to a military base in Banki near the border with Cameroon, the BBC's Stephanie Hegarty reports from Lagos.
The released Chibok girls were taken to a military base
Aid group ICRC acted as an intermediary between the government and Boko Haram
The released girls later arrived at a medical centre in Abuja for a check-up
Some were visibly tired after their ordeal
Our reporter says that many families in Chibok will be rejoicing at this latest news, but more than 100 of the girls taken have yet to be returned.
Christian pastor Enoch Mark, whose two daughters were among those kidnapped, told Agence France-Presse: "This is good news to us. We have been waiting for this day. We hope the remaining girls will soon be released." It was unclear whether his daughters had been freed.
Some of the girls pictured in May 2014, shortly after their kidnapping
A statement from a spokesman for President Buhari said he was deeply grateful to "security agencies, the military, the Government of Switzerland, the International Committee of the Red Cross, and local and international NGOs" for playing a role in the operation.
In a later BBC interview, presidential spokesman Garba Shehu added: "With all of these things together we negotiated over a period of several months, and at the end of it some of their (Boko Haram's) members were exchanged for the 82 girls."
After the Government Girls Secondary School in Chibok, Borno state, was raided in April 2014, more than 50 girls quickly escaped and Boko Haram then freed another 21 last October, after negotiations with the Red Cross.
The campaign for the return of the girls drew the support of then US First Lady Michelle Obama and many Hollywood stars.
Last month, President Buhari said the government remained "in constant touch through negotiations, through local intelligence to secure the release of the remaining girls and other abducted persons unharmed".
Twenty-one girls were released last October
Many of the Chibok girls were Christian, but were encouraged to convert to Islam and to marry their kidnappers during their time in captivity.
Boko Haram has kidnapped thousands of other people during its eight-year insurgency aimed at creating an Islamic caliphate in north-eastern Nigeria.
More than 30,000 others have been killed, the government says, and hundreds of thousands have been forced to flee from their homes.
Boko Haram at a glance:
- Founded in 2002, initially focused on opposing Western-style education - Boko Haram means "Western education is forbidden" in the Hausa language
- Launched military operations in 2009
- Thousands killed, mostly in north-eastern Nigeria, hundreds abducted, including hundreds of schoolgirls
- Seized large area in north-east Nigeria, where it declared a caliphate
- Joined so-called Islamic State, now calls itself IS's "West African province"
- Regional force has now retaken most of the captured territory
- Group split in August after rival leaders emerged