Cooley, driving the forklift, was found guilty of cruel conduct
L/Cpl Mark Cooley, 25, was jailed for two years, Cpl Daniel Kenyon, 33, received an 18 month sentence and L/Cpl Darren Larkin, 30, 140 days.
Britain's top soldier, General Sir Michael Jackson, apologised on behalf of the Army to the abused Iraqis.
The men's lawyers said they had been made "scapegoats" for the abuse.
Photos of the incidents at Camp Bread Basket, Basra, in May 2003, have been shown all over the world.
General Sir Michael said a "senior, experienced officer" would be appointed to assess "what lessons we need to learn" from this case and other abuse allegations.
He said he had been "appalled and disappointed" by the photos.
Defence Secretary Geoff Hoon said he had been "profoundly disturbed" by the case and that it was right "to apologise on behalf of the Army to the victims and the people of Iraq".
Both emphasised that the guilty men were not representative of the wider British Army.
But one of the soldiers' lawyers said his client felt that "a significant number of other soldiers, including many senior to him, some of whom have been promoted, were involved in the mistreatment of Iraqis that day".
The fate of the soldiers from the 1st Battalion The Royal Regiment of Fusiliers was decided by Judge Advocate Michael Hunter and a panel of seven senior officers.
'Terrified' prisoner
The abuse came to light when photographs taken by a fourth soldier, Gary Bartlam, were left in a Staffordshire shop to be developed.
Cooley was found guilty on two charges - one of disgraceful conduct of a cruel kind after he drove a forklift truck with a bound Iraqi suspended from the prongs.
In passing sentence, the judge told him he had "used the prisoner to amuse himself" and "that man was absolutely terrified".
He had told the court that he was moving the man out of the sun's glare.
He was also convicted of simulating a punch in a picture. His two-year sentence was the maximum possible.
General Sir Michael said the case of the men and four other cases of alleged abuse against Iraqis had to be put in the context of the actions of thousands of British servicemen.
He said he did not believe in the concept of an "endemic rotten apple" in the British Army.
'Trophy photographs'
Kenyon, the most senior soldier on trial, was found guilty of failing to report that a soldier under his command had caused an Iraqi detainee to be raised on the forks of a forklift truck.
In passing sentence, the judge told Cpl Kenyon "you were part of a scheme to produce trophy photographs".
He was also convicted of aiding and abetting Larkin to assault a prisoner.
And he was found guilty of failing to report that soldiers under his command had forced two naked prisoners to simulate sex.
Larkin pleaded guilty to one charge of assault
However, Kenyon was found not guilty of two charges of aiding and abetting unknown persons to force the detainees to simulate a sex act.
Larkin was sentenced to nearly five months after pleading guilty to assault after he was pictured standing on top of an Iraqi.
In their defence, the soldiers claimed that the abuse stemmed from an unlawful mission which took place at the aid camp to capture and deter looters.
The mission, codenamed Operation Ali Baba, was ordered by the camp's commanding officer Maj Dan Taylor.
Maj Taylor told his troops that the looters should be "worked hard", to try to stop them returning to Camp Bread Basket.
Prosecutors said the operation was in breach of the Geneva Convention.
General Sir Michael said that although no criminal action had been taken against Maj Taylor, "administrative action" remained a possibility.
And he denied assertions by the guilty trio's legal team that they had been made scapegoats, with more senior officers escaping justice.
In a separate court martial last year, the soldier who took the photos, Bartlam, admitted taking photographs of the Iraqis simulating sex acts.
Bartlam had been due to stand trial alongside the three soldiers but his lawyers negotiated a plea bargain which saw four of seven charges against him dropped.
He was sentenced to 18 months in a youth detention centre and disgracefully discharged from the Army.
The three British soldiers in the centre of an Iraqi abuse scandal have been jailed for between 140 days and two years and all three have been dismissed from the army. L/Cpl Mark Cooley, 25, Cpl Daniel Kenyon, 33, and L/Cpl Darren Larkin, 30, assaulted a number of Iraqi prisoners in Camp Bread Basket, near Basra. 

Gen Sir Michael Jackson said that he wanted to, "place on record how appalled and disappointed I was when I first saw those photographs at the outset of the trial", and has said he apologised "to those Iraqis who were abused" and to Iraq as whole. 

The men said they felt they were scapegoats as they felt they were other soldiers in the abuse and one of the men's lawyers said there was, "a significant number of other soldiers, including many senior to him, some of whom have been promoted, were involved in the mistreatment of Iraqis that day".

In a separate court martial last year, the soldier who took the photos used as evidence in the trial, Gary Bartlam, admitted taking photographs of the Iraqis simulating sex acts. He was sentenced to 18 months in a youth detention centre and disgracefully discharged from the British Army.