A statement from the Nigerian government said 82 girls were released after "lengthy negotiations" and in exchange for some suspected members of the Islamic militant group who were being held by authorities.
At the initial release of girls in October, the government said the release of another 83 would be coming soon.
Boko Haram, which previous year pledged loyalty to Islamic State, has kidnapped hundreds of men, women and children in its campaign to carve out a mediaeval Islamist caliphate.
Almost 200 of the schoolgirls had remained captive after the first negotiated release of 21 girls in October.
The source told Xinhua news agency late Saturday that the girls were released following a negotiations between the extremist group and the Nigerian government. Officials said Rakiya Abubakar was found with a six-month-old baby.
"The location of the girls kept changing since yesterday when the operation to rescue them commenced", said the official, who spoke on condition of anonymity because he was not authorized to make the announcement.
Although the Chibok girls are the most high-profile case, Boko Haram has kidnapped thousands of adults and children, many of whose cases have been neglected. He told Reuters then that the government was already negotiating with a Boko Haram splinter group for the release of more girls.
Buhari late past year announced Boko Haram had been "crushed", but the group continues to carry out attacks in northern Nigeria and neighbouring countries. Associated Press writers Bashir Adigun in Abuja, Nigeria, and Hilary Uguru in Warri, Nigeria, contributed.
A military source said the girls were now in Banki near the Cameroon border for medical checks before being airlifted to Maiduguri, the capital of Borno state.
The kidnapping was one of the high-profile incidents of Boko Haram's insurgency in Nigeria's northeast, now in its eighth year and with little sign of ending. They were in military custody late Saturday.
A Nigerian official says more of the Chibok schoolgirls have been released three years after their abduction by Boko Haram extremists, though the exact number is not immediately known.
More than 200 schools girls were seized by armed men who stormed their dormitories on the night of April 14, 2014, at the Girls Secondary School in Chibok.
The group representing the families of the girls said they were awaiting direct confirmation from the government. Though the government denied prisoner swap took place on that occasion, multiple sources, however, insisted that four Boko Haram prisoners were freed in order to secure the release of the girls.