Twenty-one newly freed Chibok girls, kidnapped by Boko Haram in 2014, met with Nigerian Vice President Yemi Osinbajo on Thursday in Abuja.
The release of the girls is "very exciting news for the whole country," he said.
Osinbajo denied press reports that the girls had been swapped for four captured Boko Haram militants.
Information Minister Alhaji Lai Mohammed called the girls' release "the product of painstaking negotiations and trust on both sides."
The International Red Cross and the Swiss government brokered the talks that led to freedom for the 21. Nigerian officials said talks with Boko Haram for the remaining captive girls would continue.
The names of all 21 girls will be released as soon as their families are contacted. Information on their health has also not been disclosed, but one of the girls is pregnant.
Mohammed thanked all Nigerians for their support and for "never losing confidence in the ability of Mr. President [Muhammadu Buhari] to secure the safe release of our Chibok girls."
Buhari, who is traveling to Germany on official business, said on Twitter he had been briefed on the girls' release before departing. "I welcome the release of 21 of our Chibok girls, following successful negotiations," he said.
Boko Haram kidnapped nearly 300 girls from a secondary school in the Borno state town of Chibok in April 2014. Dozens escaped, but 219 remained captive.
These were the first of the Chibok girls to be rescued as a result of government action.
Buhari has repeatedly vowed to rescue the girls and crush Boko Haram, which has frequently attacked schools as part of its seven-year insurgency in northeastern Nigeria, aimed at setting up an Islamic state.
The group, whose name is roughly translated as "Western education is forbidden," has been blamed for about 20,000 deaths in the region since 2009.