|The school in Chibok from where almost 300 girls were abducted in April|
The militants have repeatedly targeted villages around Chibok over recent months.
Boko Haram says it is fighting to create an Islamic state in Nigeria.
A senator for Borno state, Ali Ndume, told the BBC Hausa service that security forces posted in the town ran away when the insurgents attacked.
That's normal procedure for most Boko Haram attacks. Why can't adequate resources be assigned to protect these towns? One begins to suspect collusion between the military, the government, and Boko Haram; or, at the very least, complete indifference. In either case, major reforms are necessary in both Nigeria's military and government, but corruption is so all-pervasive it would require a major act of God to turn things around.
Residents told the Sahara Reporters news website that the militants headed to the centre of Chibok and declared that they were taking it over as part of their caliphate.
|Abubakar Shekau - leader of Boko Haram|
Since the kidnapping people have complained that the area was not well protected and many residents of Chibok had already moved to safer parts of the country, fearing another attack.
The BBC's Will Ross reports from Nigeria that the military has repeatedly failed to defend towns and villages in the north-east, allowing Boko Haram to steadily expand the area they control.
The crisis in Nigeria is deepening every week, but politicians appear more focused on next year's elections, our correspondent says.
Boko Haram has changed tactics in recent months by holding on to territory rather than using hit-and-run attacks that have left thousands dead.
Last month, the group dismissed the government's claims to have agreed a ceasefire. The government had said the ceasefire would set the stage for the release of the Chibok schoolgirls.
Chibok is a relatively small, mainly Christian town.
Its seizure comes a day after a government helicopter came down in Yola, in north-east Adamawa State - the second military helicopter to go down in the area in a week.
Also on Thursday, officials and residents said the army had managed to recapture the town of Mubi, which was the biggest town under Boko Haram's control.