Alexander Blackman is currently in jail for shooting the fighter at close range in Afghanistan's Helmand Province on September 15, 2011, after the Afghan was seriously injured by fire from an Apache helicopter.
"There you are. Shuffle off this mortal coil... It's nothing you wouldn't do to us," Blackman was heard saying, paraphrasing Shakespeare "Hamlet", in footage captured by a camera on a soldier's helmet.
"Obviously this doesn't go anywhere, fellas. I just broke the Geneva Convention," he said to his fellow Royal Marines, a reference to international laws governing the treatment of prisoners of war.
Blackman was convicted by a court martial in 2013 and sentenced to life in prison with a 10-year minimum.
The sentence was later reduced to eight years to take into account the fact that he was suffering from combat stress disorder - the same reason given by the judges today for downgrading his conviction.
A further hearing, whose date has not been set, will decide what sentence he still has to serve.
His wife, Claire, who has spearheaded a public campaign involving best-selling author Frederick Forsyth and many veterans, said she was "delighted" by the ruling.
"This is a crucial decision and one which better reflects the circumstances my husband found himself in during that terrible tour in Afghanistan," she told reporters outside the court. She said she hoped for "a significant reduction" in Blackman's sentence.
The case marked the first time since World War II that a British soldier was convicted of a murder carried out on the battlefield.
"By doing so you have betrayed your corps and all British service personnel who have served in Afghanistan, and you have tarnished their reputation," Blackett said.
The conviction was supported by Britain's chief of the defence staff at the time, Nicholas Houghton, who said: "Murder is murder, this is a heinous crime.