Nigeria's chief of defence staff, Alex Badeh, announced the truce. Boko Haram has not made a public statement.
The group has been fighting an insurgency since 2009, with some 2,000 civilians reportedly killed this
year.
Boko Haram sparked global outrage six months ago by abducting more than 200 schoolgirls.
The girls were seized in the north-eastern town of Chibok in Borno state, and their continued captivity
has led to criticism of the Nigerian government's efforts to secure their release.
Members of the Bring Back Our Girls campaign said in a tweet on Friday: "We are monitoring the news with huge expectations."
Air Chief Marshal Badeh revealed the truce at the close of a three-day security meeting between Nigeria and Cameroon. He said Nigerian soldiers would comply with the agreement.
Nigerian presidential aide Hassan Tukur told BBC Focus on Africa that the agreement was sealed after a month of negotiations, mediated by Chad.
As part of the talks, a government delegation twice met representatives of the Islamist group.
Mr Tukur said Boko Haram had announced a unilateral ceasefire on Thursday and the government had responded.
"They've assured us they have the girls and they will release them," he said.
"I am cautiously optimistic."
He said arrangements for their release would be finalised at another meeting next week in Chad's capital, Ndjamena.
The negotiations are said to have the blessing of Boko Haram leader Abubakar Shekau, reports the BBC's Chris Ewokor in Abuja.
Speaking to the BBC, Nigerian government spokesman Mike Omeri said Boko Haram would not be given territory under the ceasefire agreement -and that the government would not reveal what concessions it would make.
"We are inching closer to release of all groups in captivity, including the Chibok girls," he said.
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