The verdict by the Supreme Court is final and cannot be appealed, a court official said, requesting anonymity because of department rules. The Defense Ministry said it confirmed the court's ruling.
The conscript, only identified by his surname Yim, had told investigators after his arrest that he assaulted fellow soldiers because he felt insulted by drawings they made of him. He had fled into the forest near the border with North Korea but was captured after a failed suicide attempt.
South Korea requires all able-bodied men to serve in the military for about two years in the face of a threat from North Korea. Shooting rampages by bullied soldiers in South Korean army barracks are not unusual.
In 2005, another soldier went on a similar rampage and killed eight colleagues in anger at superiors who he said verbally abused him. He too was sentenced to death.
Confrontations between the rivals deepened recently following the North's nuclear test and long-range rocket launch.