The Supreme Court says its verdict on Friday is final and cannot be appealed.
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.
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.
South Korean courts occasionally issue death sentences but the country has not executed anyone since December 1997.
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