It was not immediately clear where the new video was shot, but Shekau who spoke in both Hausa and Arabic said it was filmed on Christmas Day.
Shekau last appeared in a video in September where he disputed a claim by the Nigerian military that he had been wounded in battle.
He vowed to continue fighting on until an Islamic state was imposed in northern Nigeria.
“Our aim is to establish an Islamic Caliphate and we have our own Caliphate, we are not part of Nigeria.”
Buhari had announced that a months-long military campaign in the 1,300 square-kilometre (500 square-mile) forest in northeastern Borno state had led to the “final crushing of Boko Haram terrorists in their last enclave in Sambisa Forest”.
The government in Abuja and the military have frequently claimed victories against the Islamic State group affiliate but access to the epicentre of the conflict is strictly controlled.
That has made independent verification of official statements about victories virtually impossible.
Attacks have meanwhile continued, making claims of defeating Boko Haram questionable despite undoubted progress in pushing back the group.
The Boko Haram’s insurgency has killed at least 20,000 and forced some 2.6 million others to flee their homes since 2009.
The violence has sparked a dire humanitarian crisis in the region, with thousands of children facing the risk of famine and starvation.