"Thanks be to Allah who gave victory to our brethren in (the town of) Gwoza and made it part of the Islamic caliphate," Abubakar Shekau said in the 52-minute video obtained by AFP.
He declared that Gwoza, in Borno state, now has "nothing to do with Nigeria".
"By the grace of Allah we will not leave the town. We have come to stay," said Shekau, who has been designated a global terrorist by the United States and sanctioned by the UN Security Council.
Boko Haram is also believed to be in control of other areas near Gwoza in southern Borno, as well as large swathes of territory in northern Borno and at least one town in neighbouring Yobe state.
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Mapping the precise areas which have fallen into Islamist hands is nearly impossible.
There are few humanitarian workers on the ground in the northeast, travel is dangerous and the region, which has been under a state of emergency since May of last year, has poor mobile phone coverage.
But many analysts believe the military has the capacity to reverse the insurgents' advance.
Soldiers this week refused to deploy to Gwoza without better weapons in an apparent mutiny.