"Initially, three soldiers were arrested while they were still deployed in the Far North" province fighting the Nigerian jihadist group, one of the sources told AFP.
The three were directly implicated in the video, which went viral, the source said.
"They were from the air force and were deployed in Mabass," a village in Far North province near Nigeria where Boko Haram is based.
Questioning of the three led to the arrest of a fourth soldier who was not present at the execution but who played a role in it, the source said, without elaborating.
Investigators are seeking to learn whether the execution was an isolated event or part of a broader pattern.
Another source close to the army, speaking from the Far North capital Maroua, told AFP: "Within the army, here in this region, there is no doubt as to the video's authenticity. Some soldiers clearly expressed their disapproval to their colleagues who were implicated."
The Cameroonian army is deployed in the region to counter frequent incursions by Boko Haram fighters from Nigeria.
On July 11, the day after the video emerged, the Cameroonian government announced an investigation, though it branded the video "fake news" and a "horrible montage".
Amnesty International for its part said it had "credible evidence" that the men in the video were Cameroonian soldiers.
On Wednesday, Britain said it was "deeply concerned" by the footage, urging President Paul Biya to open an "urgent investigation".
The day before, Washington also called for an investigation, urging the Cameroon government to "make its findings public, and if Cameroonian military personnel were involved in this atrocity, hold them accountable."
Aid groups regularly accuse the Cameroonian army of carrying out exactions against people suspected of belonging to Boko Haram, charges it has consistently denied.
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