The insurgents attacked and seized the town on Thursday evening, residents said.
The attackers have repeatedly targeted villages around Chibok over recent months.
A senator from Borno State, Ali Ndume, told the BBC Hausa service that security forces deployed in the town ran away when the insurgents attacked.
Residents said the insurgents headed to the centre of Chibok and declared that they were taking it over as part of their caliphate.
The insurgents have changed tactics in recent months by holding on to territories rather than using hit-and-run attacks that have left thousands dead.