The random killing of Jo Jung-Pil was made into a hit movie in 2009, reviving public anger over the crime and forcing South Korean prosecutors to reopen the case.
Arthur Patterson, now 37, was convicted by a Seoul court last year and the Supreme Court of Korea upheld the ruling Wednesday, adding in a statement that his sentence was "justified".
Patterson, the son of a US military contractor, was 17 at the time, and 20 years in jail is the maximum penalty in South Korea for an offender under 18.
Patterson was tried and convicted in 1997 as an accomplice to Edward Lee, a Korean-American man, who was jailed for 20 years for murder. Each accused the other of killing Jo.
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Patterson served 18 months in prison for lesser charges including obstruction of justice, and was released in 1998 as part of an amnesty programme, only to find himself a murder suspect again after Lee was acquitted on appeal for lack of evidence.
He fled to the United States a year later after investigators failed to renew his travel ban -- a mistake that sparked a storm of criticism.