Negotiations with the extremist group, mediated by the International Committee of the Red Cross and the Swiss government, also resulted in the October release of a first group of 21 Chibok girls.
The girls who were freed on Saturday are undergoing rehabilitation similar to that of their peers who were released in October.
The released girls are now in the care of the government's women's affairs ministry.
This was the second release of schoolgirls since the electoral defeat of former President Goodluck Jonathan, scored for his failure to lead an immediate and thorough search for the students, many of whom were forced to take militants as husbands and bear their children.
"The president made a promise that he will educate them", he said, adding that parents of the girls were anxious about having to pay for their schooling if it was not covered by the state.
She says Nigeria's government has no regrets about exchanging Boko Haram detainees for the 82 young women released over the weekend.
Reports of the kidnapping sparked global outrage and a massive social media campaign led by Nigerians, catching the attention of many globally known activists and celebrities.
She said already, the recently released 82 girls are now undergoing rehabilitation and reintegration processes in various medical facilities across the Federal Capital Territory, FCT.
The girls said they wanted to go back to school so a nine-month reintegration program was designed for them, the minister said.
"It's important to remember that these young women are not prisoners". We will never prevent them from seeing their daughters.
Nigeria's presidency has released the names of the 82 Chibok schoolgirls newly freed from the Boko Haram extremists. "They gave government consent for them to be here", she said. They instead had to stay in a state safe house under armed escort, relatives said.
"Parents' involvement is crucial", said Aisha Muhammed-Oyebode, a leader of Bring Back Our Girls and head of the Murtala Muhammad Foundation, a nonprofit organization supporting the parents of the abducted girls. We will do it again if needed.
Addressing the mammoth crowd of celebrants on behalf of the army at the Army Headquarters Garrison, Abuja, Lt Col Adamu Usman, promised that the Nigerian military will do all within its powers to ensure that every Nigerian being held in captivity is released and allowed to join their families to continue their normal life in the society.
"As with all children who have suffered the trauma of being held by the insurgents, the need for psychosocial support is likely to be long term and will need to be assessed on an individual basis", said UNICEF spokeswoman Doune Porter.