The footage was shot during the final stages of the Sri Lankan army's battle against the separatist Liberation Tigers of Tamil Eelam (LTTE).
Alston said three US-based independent experts he had commissioned to conduct an impartial evaluation established the authenticity of the video after four Sri Lankan specialists had concluded that it was a fake.
He named the three as Daniel Spitz, a prominent forensic pathologist, Peter Diaczuk, a firearm evidence expert, and Jeff Spivack, a forensic video analyst.
"The independent experts' analyses also systematically rebutted most of the arguments relied upon by Sri Lanka's experts in support of their contention that the video was faked.
"In light of these conclusions, I call for an independent inquiry to be established to carry out an impartial investigation into war crimes and other violations of international humanitarian and human rights law allegedly committed in Sri Lanka."
Colombo should ask the UN to set up an independent commission of inquiry, he said.
The footage shows a man dressed in army uniform shooting a naked, bound and blindfolded man in the back of the head, while eight other bodies can be seen nearby in a muddy field.
Alston said Spitz found the footage appeared authentic "especially with respect to the two individuals who are shown being shot in the head at close range".
And he added that Spivack's forensic video analysis "found no evidence of breaks in continuity in the video, no additional video layers and no evidence of image manipulation."
"While there are some unexplained elements in the video, there are strong indications of its authenticity," Halston said.
"In addition, most of the arguments relied upon by the government of Sri Lanka to impugn the video have been shown to be flawed."
The Sri Lankan military has said the video was faked in order to discredit the security forces.
Sri Lankan authorities have resisted international calls for a war crimes investigation after the UN alleged that more than 7,000 civilians had been killed during the first four months of 2009 alone.
Tamil forces were finally vanquished in May after nearly four decades of ethnic bloodshed that left between 80,000 and 100,000 people dead.
The government victory ended the LTTE's four-decade struggle for an independent Tamil homeland in the island's northeast, one of Asia's longest-running ethnic conflicts.