"Shuffle off this mortal coil ... It's nothing you wouldn't do to us," the marine was heard saying in a video that captured the incident. The footage was inadvertently recorded by a camera mounted on the helmet of Marine B.
He then turned to his comrades identified only as Marines B and C and said: "Obviously this doesn't go anywhere, fellas. I just broke the Geneva Convention."
Marine B then replied: "Yeah, roger, mate."
Earlier in the trial, prosecutors called the killing a "field execution."
The soldiers told their superiors that the man had died from wounds, but the killing came to light when police investigating other matters found the video on a soldier's laptop. Footage was shown at the court martial.
The three denied murdering the Afghan, and one marine had said he believed the man was already dead.
But a seven-member board convicted Marine A after a two-week trial. The two other marines were acquitted of "encouraging and assisting" in the killing.
The convicted soldier will be sentenced on Dec. 6. The maximum sentence is life imprisonment.
British forces have been fighting the Taliban in Afghanistan alongside other international forces since 2001. The U.K. plans to end its combat role there by the end of 2014.