Speaking into the camera, the man says he coordinated with the two gunmen who attacked the Charlie Hebdo magazine on Wednesday, killing 12.
"I am addressing myself first of all to the Caliph of Muslims Abu Bakr al-Baghdadi," he says, referring to the leader of IS.
"I have declared allegiance to the Caliph," he says in broken, stuttering Arabic, wearing Islamic white dress and headgear.
"The brothers of our team, they did Charlie Hebdo," the man says.
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"I also went out a bit against the police so that it has more impact. We managed to synchronise to come out at the same time," he says, wearing a camouflage army vest in this section.
The video starts with shots of the man doing press-ups in sports gear. An automatic rifle leans against the wall beside him in a later section.
Coulibaly died when police launched an assault on the Jewish supermarket in eastern Paris, where four hostages were killed.