Kevin Williams, 22, was charged last September with killing lawyer Hassan Abbad Sayed in August 2003 at a checkpoint near Basra. Sayed was armed with a pistol at the time, but, according to his family, he had a British-issued license to carry firearms to protect himself against criminals at a time of widespread lawlessness.
Although military officials initially decided against trying Williams in a court martial, Scotland Yard opened its own investigation, and he was charged.
However, the director of public prosecutions reviewed the evidence and decided there was no case.
The case marks the first time Attorney General Lord Peter Goldsmith QC, has overruled the military over a prosecution, the newspaper said.