The allegations centred on the the Argyll and Sutherland Highlanders, 5th Battalion, The Royal Regiment of Scotland's tour of duty in Afghanistan between September 2010 and April 2011.
The unit served as part of Operation Herrick 13, and it was claimed fingers of members of the Taliban were collected and kept as trophies.
The case was referred to the independent Service Prosecuting Authority, which investigated the three service personnel for the offence of "outrages upon personal dignity", under the War Crimes section (Article 8) of the International Criminal Court Act 2001, (Elements of Crime) Regulations 2004.
In response to a request for information, the Ministry of Defence said: "After consideration, the director of service prosecutions directed that no charges should be brought against any of the three individuals, due to insufficient evidence."
The MoD said internal administrative action was also considered against the three individuals but the information relating to this was not released because it is protected by the principles of the Data Protection Act 1998.
At the time the investigation came to light in August 2011, Scottish Liberal Democrat leader Willie Rennie called for urgent action to be taken over the allegations.
He said: "If these sickening acts were the result of severe military trauma, then the Army needs to act quickly to ensure that others are not suffering in this way."
The Special Investigation Branch, the investigations arm of the MoD launched an immediate inquiry.
The claims were particularly controversial because Muslim tradition dictates a dead person must be buried with all their body parts.
If any body parts have been removed, they should be buried along with the body. General Lord Richard Dannatt, the former head of the Army, warned at the time the accusations could be "incredibly damaging" to operations in Afghanistan, whether they proved to be true or not.
He said: "The potential damage is huge. The allegation in itself is damaging even if not true because it has been published."
In 2010, a Gurkha soldier faced disciplinary action after beheading a Taliban gunman and carrying his head back to base in a bag.
The Nepalese soldier apparently made the decision to remove the head in a misunderstanding over the need for DNA evidence of the kill.
His unit had been told they were seeking a high-value target, a Taliban commander, and they must prove they had killed the right man.
Sources claimed at the time the soldier, who was in his early 20s, had told investigators that he unsheathed his kukri after running out of ammunition. The weapon symbolically belongs to the Gurkas.
It emerged the Taliban fighter was mutilated so his identity could be verified through DNA tests.
The soldier was cleared in 2011 and resumed his duties.
Britain still has 9000 troops in Afghanistan ahead of a scheduled withdrawal in 2014.
Soldiers from the Argylls, known as 5 Scots, are based at Howe Barracks in Canterbury, Kent.