Private Stuart MacKenzie, who has already faced a military court martial, escaped charges after the Crown Prosecution Service said there was insufficient evidence to gain a conviction.
He could have faced charges of obtaining property by deception, but the CPS said chances of a "realistic prospect of conviction" were slight.
Morgan resigned as the editor of the Daily Mirror in May after the paper published fake photos, allegedly showing British troops from the Queen's Lancashire Regiment abusing Iraqi prisoners.
The Daily Mirror had published the pictures sold to it by MacKenzie in good faith and had thought them genuine, but it soon emerged the photographs were fake and had been taken in the back of an Army lorry in the UK.
One photo was purported to show a Queen's Lancashire Regiment soldier urinating on an Iraqi prisoner, but doubts emerged about the authenticity of the pictures after a Royal Military Police investigation.
It emerged that the lorry pictured had never been to Iraq. MacKenzie did serve in Iraq, his TA unit was attached to the Queen's Lancashire Regiment.
However, despite widespread disbelief in military circles, the Daily Mirror refused to back down over its claims and continued to insist the pictures were the real thing. Morgan only went after they were officially shown not to be the genuine article and the Queen's Lancashire Regiment called for an apology from the Mirror.
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