Alexander Blackman, 42, shot the insurgent in Helmand province in 2011 and was convicted of murder two years later.
Five judges sitting at the Court Martial Appeal Court in London have replaced that conviction with manslaughter on the grounds of diminished responsibility.
Originally, Blackman was sentenced to life with a minimum term of 10 years - but this was later cut to eight years on appeal due to the combat stress he had been suffering at the time of the killing.
The sentence he now has to serve will be decided at a hearing which has not yet been scheduled.
Blackman's wife Claire said she was "delighted" by the decision, adding that it "much better reflects the circumstances that my husband found himself in during that terrible tour of Afghanistan".
She said: "We must now hope to secure a significant reduction in the sentence."