The soldiers, who arrested Ahmed Karheem, 15, as a suspected looter in the southern Iraqi city of Basra in May 2003, had been accused of forcing him to swim in a canal to punish him. Karheem could not swim and died, prosecutors said.
Defence lawyers said the soldiers were poorly prepared and did not number enough for the demands of patrolling a chaotic city in the weeks after the 2003 US-led invasion of Iraq that toppled Saddam Hussein.
They said the main Iraqi witness to the incident, also arrested by the soldiers, was not trustworthy.
After the hearing at a military base in Colchester in England, Jerry Hayes, a defence lawyer, said: "This case should never have been brought.
"It was a tragic accident, nothing more. What they were asked to do was convict three brave young men on the word of a confessed looter. And that's ridiculous."
The military court found guardsmen Martin McGing, 22, and Joseph McCleary, 24, and Colour Sergeant Carle Selman, 39, not guilty of manslaughter. Another guardsman, James Cooke, 22, was cleared earlier in the trial, which began last month.
A defence ministry spokesman said the soldiers were now free to resume their military duties.
Last year, seven British soldiers were cleared of murder when their trial collapsed because the judge concluded that the Iraqi witnesses were unreliable.
A case against another seven British soldiers accused of killing an Iraqi hotel receptionist is due to be heard this year.
Three British soldiers were convicted last year of abusing Iraqi prisoners.