The man said to be Abubakar Shekau said people were killed “as our Lord instructed us”, threatening more raids.
He taunted nearby countries’ leaders.
Some reports said that as many as 2,000 people died in the Baga raid but Nigeria’s government has disputed this, putting the toll at just 150.
“We killed the people of Baga,” the man claiming to be Shekau said in the 35-minute video, quoted by AFP news agency.
He also issued a challenge to Nigerian and regional forces to attack his group.
The video displayed an array of weapons believed to have been taken from a military base in neighbouring Doron Baga.
Boko Haram has seized control of towns and villages in north-east Nigeria and has begun threatening neighbouring countries.
The video has not been verified but correspondents say it was in typical Boko Haram style, with the group’s leader in combat fatigues and surrounded by masked fighters.
Satellite images released by Amnesty International showed widespread destruction in Baga and Doron Baga in the far north-east of Nigeria, with some 3,700 buildings damaged or destroyed.
Amnesty cited witnesses saying that militants had killed indiscriminately and described the damage was “catastrophic”.
The rights group said the attack was the largest and deadliest by Boko Haram that it had analysed.
A businessman from Baga told the BBC people were being killed like animals. He said he fled the town along with some 5,000 others.
Hundreds of women and children were reported to have been taken captive.
The upsurge in violence has alarmed Nigeria’s neighbours, particularly in Cameroon.In the latest reports of fighting, “heavy clashes” were said to have taken place in Bonderi in the far north of Cameroon, near the Nigerian border on Tuesday night.
Suspected Boko Haram militants were believed to have kidnapped dozens of people in a cross-border raid near Mokolo city in Cameroon’s Far North region last Sunday. Some were later freed as Cameroon’s forces pursued the attackers who were fleeing back to Nigeria.
Thousands of Cameroonian troops have been deployed to the north to try to stem the raids and President Idriss Deby of Chad has also sent a contingent of troops.
Meanwhile, officials from Nigeria and its neighbours met in Niger’s capital Niamey on Tuesday to discuss a regional response to Boko Haram.
One suggestion is a new force, possibly under the auspices of the African Union, to tackle the insurgents.
Nigeria is due to hold elections next month but there are growing doubts whether they can successfully go ahead in all parts of the country.