The 82 youngsters were welcomed in the capital Abuja to the official residence of Muhammadu Buhari, more than three years after they were abducted from the village of Chibok.
Presidential adviser 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 74 year old leader of Africa's most populous country left shortly after the meeting, for medical checks in London as concerns over his health continue.
Parents including Rev Enoch Mark, whose two daughters were abducted, have faced an anxious wait to learn whether their children are among the freed.
Rev Mark said he considered all 82 of the girls to be his daughters "because most of them worship in my church".
Their release was negotiated between the International Red Cross and the Swiss Government. Five commanders at Boko Haram were released in exchange.
The girls were among 276 youngsters abducted in 2014 by the extremist group Boko Haram, which has links to the Islamic State group.
Pernille Ironside, acting representative of Unicef Nigeria, said: "They will face a long and difficult process to rebuild their lives after the indescribable horror and trauma they have suffered at the hands of Boko Haram."
Over the last eight years, an uprising by Boko Haram has left more than 200,000 people dead and 2.6 million forced from their homes.