The girls, most of them Christians, were taken from their classroom in the town of Chibok six months ago.
Nigeria's chief of defence staff, Alex Badeh, announced the deal.
He said: "A ceasefire agreement has been concluded between the Federal Government of Nigeria and the Jama'atu Ahlis Sunna Lidda'awati wal Jihad [Boko Haram].
"I have accordingly directed the service chiefs to ensure immediate compliance with this development in the field."
What is Boko Haram?
- Founded in 2002
- Means "Western education is forbidden"
- Tried to create Islamic State in 2009
- Has killed thousands of people across Nigeria
Pastor Jonathan Oloyede, convenor of the National Day of Prayer & Worship, has campaigned for the girls' release.
He said: "We pray for the full recovery of these girls from the trauma of what they have gone through.
"They will have been exposed to all kinds of extremes of Islam and they may have been taken through some degree of rituals and confessions, but all of these things are reversible."
He added: "If these reports are authentic we rejoice that these girls are going to be released and we pray that the parents and the families and the loved ones will be able to get over the horrors and the challenges of these many months."
Negotiations between the government and Boko Haram have been ongoing for the past month and both sides have agreed to a truce.
In the past, Boko Haram has offered to free the girls if the government agreed to release some of its fighters from prison.
Pastor Oloyede said: "We pray that they won't have compromised in any way with the terrorists.
"We pray that the Nigerian government will be strong and ethical in everything it did to release these girls.
"We hope that this is not a false piece of information and we pray that the girls be released."
Speaking to the BBC, Nigerian presidential aide Hassan Tukur said: "They've assured us they have the girls and they will release them.
"I am cautiously optimistic."
An international campaign calling for the release of the girls led to protests in major cities.
At one point, the hashtag #BringBackOurGirls was trending worldwide and US First Lady Michelle Obama tweeted about the kidnappings.
The UK government has sent experts to Nigeria to assist in the search for the students and an RAF aircraft was deployed.
President Obama also sent a team of military officers specialising in "intelligence, investigations, hostage negotiation, information-sharing and victim assistance".
Listen to Premier's Des Busteed's full interview with Pastor Jonathan Oloyede: