In a 115-page document to be presented to the US Senate, Asif Iqbal, Ruhal Ahmed and Shafiq Rasul, who were released in March, allege they were abused, tortured, forcibly injected with drugs and humiliated.
Details from the document were released to the British media on Wednesday, before formal presentation to the Senate Armed Services Committee.
"The account they've given from start to finish of their time in detention is an account of systematic brutality, a systematic coerced attempt to obtain confessions," their lawyer, Gareth Pierce, told BBC radio.
Pierce also mentioned that the abuse included "interrogation carried out in ways that are banned by the international community, by treaty obligations, and enforced isolation which induced a sense of wholesale desperation, hopelessness and helplessness".
The men, known in Britain as the Tipton Three after the town in the English West Midlands where they live, say they were repeatedly punched, kicked, slapped, forcibly injected with drugs, deprived of sleep, hooded, photographed naked and subjected to body cavity searches and, sexual and religious humiliations.
More than 600 detainees are held
at Guantanamo without charge
One of them claimed a British interrogator, from the elite SAS, was present when a US soldier pointed a gun at his head and threatened to shoot.
After Major-General Geoffrey Miller took charge of the camp, new practices such as the shaving of beards, playing loud music, shackling detainees in squatting positions and locking them naked in cells were introduced.
Britain's Ministry of Defence said it would investigate the allegations.
The men said a US guard told them: "The world does not know you're here. We would kill you and no one would know."
On arrival back in Britain, the men were detained by police but soon freed without further legal proceedings.
US authorities originally held nine British citizens, most of them detained in Afghanistan.
Five were released in March without facing further legal proceedings.
Four remain in custody at Guantanamo Bay. There are also four men of non-British nationality, but who are registered residents in Britain, still imprisoned at the base.
The detentions have caused widespread disquiet in Britain, with lawyers for the detained men referring to a "legal black hole".
Law Lord Johan Steyn, the third most senior Lord of Appeal in Ordinary, said two years ago: "Our [British] government ought to make plain publicly and unambiguously our condemnation of the utter lawlessness at Guantanamo Bay."