The 82 girls were freed Saturday in exchange for an unspecified number of detained Boko Haram suspects, Buhari's office said in a statement.
Mr. Buhari also said he was pleased to have personally met the girls and assured them that the presidency will personally supervise the performance of those entrusted with their welfare.
The Bring Back Our Girls campaign said Sunday it was happy that Nigeria's government had committed to rescuing the 113 remaining schoolgirls, and it urged the president to "earnestly pursue" the release of everyone held by Boko Haram.
The girls were received on behalf of the president at the Abuja airport by the Chief of Staff Abba Kyari when they descended from a Nigerian air force military carrier.
"One of the girls was carrying a baby with her, a boy of less than two years", said the source on condition of anonymity.
The International Committee of the Red Cross has tweeted what might be the first public image of the Chibok schoolgirls freed by Boko Haram extremists. The photo showed a line of young women wearing shirts with the ICRC logo waiting to board a helicopter.
He did not comment on how many imprisoned members of Boko Haram - whose fight to create a hardline ISIS in northeast Nigeria has left at least 20,000 dead since 2009 - had been released in the swap.
The ICRC said it had acted as a neutral intermediary to transport the girls into Nigerian custody. Neither Nigeria's government nor Boko Haram, which has links to the Islamic State group, gave details about the exchange.
The first batch of 21 were freed last October with the aid of the Red Cross and Switzerland.
Boko Haram fighters stormed the Government Girls Secondary School in Chibok on the evening of April 14 2014 and kidnapped 276 teenaged girls.
ICRC deputy regional coordinator Patrick Youssef says the 82 girls soon will meet with their families.
The victims arrived in Nigerian capital on Sunday to meet with the Nigerian president Muhammadu Buhari, according to an official.
Shehu Sani, a Nigerian senator who has been involved in previous negotiations, said the talks lasted for "three to four months".
A Nigerian military official with direct knowledge of the rescue operation said the freed girls were found near the town of Banki in Borno state near Cameroon.
Until their release, 195 girls were estimated to be in the hands of the terrorist group led by Abubakar Shekau. Now 113 girls remain unaccounted for.
Islamist militant group Boko Haram released 82 Chibok schoolgirls who were kidnapped by the organisation three years ago.
One of his advisers, Femi Adesina, said: "The president was delighted to receive them and he promised that all that is needed to be done to reintegrate them into the society will be done".
The president said the schoolgirls were freed in exchange for detained suspected extremists in the largest negotiated release so far of the almost 300 girls whose mass abduction in 2014 highlighted the threat of Nigeria's homegrown extremist fighters who are linked to the Islamic State group.