There had been no previous claim of responsibility for the bombings, which killed 34 people and heightened security fears before next month's Winter Games.
In the video, two Russian-speaking men warned President Vladimir Putin that "If you hold these Olympics, we will give you a present for the innocent Muslim blood being spilled all around the world: In Afghanistan, in Somalia, in Syria." They added that "for the tourists who come, there will be a present, too."
In a statement posted with the video on its website, the militant group Vilayat Dagestan yesterday claimed responsibility for the Volgograd bombings.
The video claims that the two men, identified as Suleiman and Abdurakhman, were the suicide bombers and purports to show the explosives being prepared and strapped to their bodies.
There was no immediate reaction to the video from the Russian security services.
During much of the 49-minute video, the two men speak to the camera while holding Kalashnikov automatic rifles. Behind them hang black banners with Arabic religious phrases similar to those used by al-Qaida.
Vilayat Dagestan is one of the groups that make up the so-called Caucasus Emirate, which seeks to establish an independent Islamic state in the North Caucasus, a region just to the east of Sochi on Russia's southern border.
Dagestan, one of several predominantly Muslim republics in the North Caucasus, has become the centre of the Islamic insurgency that has spread throughout the region following separatist wars in neighboring Chechnya.
In response to the terrorist threat, Russia has introduced sweeping security measures for the Sochi Games.
The Chechen leader of the Caucasus Emirate, Doku Umarov, had ordered a halt to attacks on civilian targets in 2012, but he rescinded that order in July and urged his followers to try to undermine the Olympics.