Judge Advocate Michael Hunter made the announcement on Friday after a seven-member panel of officers found the three men guilty earlier in the week.
The most senior of the trio, Corporal Daniel Kenyon, 33, was given an 18-month sentence after being found guilty of three charges including failing to report the mistreatment of the captured looters at an aid camp near Basra in May 2003.
A panel of seven officers and a judge at the court martial in an army barracks sentenced Lance Corporal Mark Cooley, 25, to two years in prison after he was found guilty of disgraceful conduct of a cruel kind for driving a forklift truck with a bound Iraqi suspended from the prongs.
Cooley drove a fork lift truck with
an Iraqi detainee bound to it
A photograph of the helpless Iraqi dangling from the forklift was among a series of photographs taken by soldiers at the aid camp known as Camp Bread Basket.
In the verdicts which were given on Wednesday, Cooley was also convicted of simulating a punch on an Iraqi.
The third defendant, Lance Corporal Darren Larkin, 30, was sentenced to five months in jail after he pleaded guilty to assault. He had been pictured standing on an Iraqi.
All three soldiers were also dishonorably discharged from the army.
The case drew comparison with the Abu Ghraib scandal involving US troops.
The British case came to light when another soldier was arrested with photographs depicting scenes of mistreatment including some in which soldiers had apparently forced naked Iraqi detainees to simulate sodomy and oral sex.