The soldiers, all members of the 3rd Battalion of the Parachute Regiment, have been found not guilty of murder and violent disorder.
The soldiers were standing trial accused of murdering 18-year-old Nadhem Abdullah in an attack on a group of Iraqi civilians in al-Ferkah, 60 miles north of Basra, in May 2003.
Judge Advocate General Jeff Blackett today directed the military panel hearing the court martial in Colchester, Essex, to clear the seven defendants of all charges against them.
He said: "In relation to all the defendants, after discarding the evidence that is too inherently weak or vague for any sensible person to rely on it, prosecution evidence taken at its highest is such that a reasonable jury or court martial board properly directed could never reach the high standard of proof required to be sure of the guilt of any defendant.
"In those circumstances it is my duty to remove the case from the board now and direct that they return verdicts of not guilty to the charge of murder against all seven defendants."
During the trial Martin Heslop QC, prosecuting, told the court that Mr Abdullah was an "innocent" teenager who died after being subject to a gratuitously violent attack during which the paratroopers used their rifle buts, helmets, fists and feet.
The court heard that blood matching the dead man's DNA was found in a screw recess on Private Samuel May's rifle.
The cleared soldiers are Corporal Scott Evans, 32, Private Billy Nerney, 24, Samuel May, 25, Morne Vosloo, 26, Daniel Harding, 25, Roberto Di-Gregorio, 24, and Scott Jackson, 26.
Before directing the panel to clear the soldiers, Judge Blackett said he considered the investigation into the case had been "inadequate".
He said: "It has been established during the course of the case that the investigators made serious omissions in not searching for records of hospital admissions or treatment and not establishing whether there was a register at Al Najaf shrine in which Nadhem's burial may have been recorded."
Judge Blackett also criticised investigators for not taking DNA swabs from Nadhem's siblings to exclude them as a possible source of the blood on Private May's rifle and for not analysing the DNA swabs taken from the defendants.
He also said it had been a "significant error" to have waited six months before interviewing the defendants under caution or taking fuller statements from the Iraqi witnesses.
Judge Blackett said that the Iraqi witnesses had admitted using the case to obtain money from the British Army.
"They frequently spoke of 'fasil' or blood money and compensation to what were patently exaggerated claims," he said.
However, Judge Blackett said he had no criticism to make of the prosecution or the Army prosecuting authority.
During the trial, he said it became clear that the main Iraqi witnesses had exaggerated and lied about the alleged incident.
"Had the Iraqi witnesses turned out to be credible, then the case would have been stronger," he said.
Judge Blackett commiserated with Nadhem's family over his death, but said it would have been "a miscarriage of justice to blame these seven defendants collectively for that death".
A legal source at today's hearing estimated it had cost £10 million to stage the trial.
Mr Heslop QC, prosecuting, was not in court for today's decision.
Speaking after the decision, Rex Tedd, representing Corporal Evans, said: "These are very courageous men doing a very dangerous job in difficult circumstances.
"To have a charge as grave as this hanging over a man's head when he's a serving soldier is very difficult indeed.
"Corporal Evans will be going home today to his family with his head held high. His relief today is unlimited."
Christopher Hill, Private Vosloo's solicitor, said: "It's been very difficult. It's been a terrible strain. I don't think it has quite sunk in that it is all over."
Mr Hill said that Mr Vosloo had come from South Africa to join the British Army and remained "proud" of it.
"It is ironic that a few years ago he was playing cricket in South Africa with Kevin Pietersen. While Kevin Pietersen was winning the Ashes, my client had a murder charge hanging over him."