A settlement in a lawsuit against two psychologists who were paid tens of millions of dollars to design torture techniques used by the CIA in black-site prisons was announced on Thursday. The terms of the settlement were undisclosed.

Two of the plaintiffs in the case, Suleiman Abdullah Salim and Mohamed Ben Soud, were held and brutalized in 2003 in a secret CIA facility in Afghanistan that prisoners called “The Darkness”. Salim, who is Tanzanian, and Ben Soud, who is Libyan, were eventually released and are now living in their home countries with their families.

A third plaintiff is a young Afghan computer engineer whose uncle, Gul Rahman, was tortured to death in November 2002 in the same facility.

The three filed the lawsuit in October 2015 against James Mitchell and John “Bruce” Jessen, contract psychologists who devised a menu of abusive interrogation methods and billed the CIA between $75m and $81m. The plaintiffs sought damages from the men for allegedly aiding and abetting torture, non-consensual human experimentation and war crimes.

The settlement included a joint statement on behalf of the plaintiffs and defendants, in which Mitchell and Jessen acknowledged their role in developing “a program for the CIA that contemplated the use of specific coercive methods to interrogate certain detainees”.

Mohamed Ahmed Ben Soud. Photograph: ACLU

The statement records that “Gul Rahman was subjected to abuses in the CIA program that resulted in his death and pain and suffering to his family” and that Salim and Ben Soud “were also subjected to coercive methods in the CIA program which resulted in pain and suffering for them and their families”.

The psychologists asserted in the statement that the abuses that Salim, Ben Soud and Rahman endured happened without their knowledge, and the doctors denied responsibility for the prisoners’ treatment. The plaintiffs said they “stand by their allegations regarding the responsibility of Drs Mitchell and Jessen”.

“Drs Mitchell and Jessen state that it is regrettable that Mr Rahman, Mr Salim and Mr Ben Soud suffered the abuses,” the statement concludes.

For the three plaintiffs, the settlement concluded a long journey to win official acknowledgement of their ordeals.

“We brought this case seeking accountability and to help ensure that no one else has to endure torture and abuse, and we feel that we have achieved our goals,” they said in a joint statement released today.

“We were able to tell the world about horrific torture, the CIA had to release secret records, and the psychologists and high-level CIA officials were forced to answer our lawyers’ questions. It has been a long, difficult road, but we are very pleased with the results.”

Salim v Mitchell was scheduled to go to trial before a jury in Spokane Washington on 5 September 2017. A trial would have marked the first time a jury was asked to decide whether the architects of the torture program owed reparations to former prisoners.

Previous suits relating to the CIA’s interrogation program were dismissed when the Bush and then Obama administrations intervened and claimed state secrets would be at risk if the cases proceeded. But the Senate intelligence committee’s 2014 report on torture in the CIA’s black sites confirmed that the three men had been held in a facility that is codenamed COBALT in the report, and that they were among 39 men subjected to the program’s enhanced interrogation techniques. The public disclosure of what had been among the US government’s most closely guarded secrets opened the way to the lawsuit.

Even without a jury trial, the lawsuit excavated hundreds of pages of previously classified documents about the planning and operation of the CIA’s RDI program, and an evidentiary record of over 4,000 pages of exhibits.

In guiding the lawsuit through discovery and toward trial, Judge Justin L Quackenbush turned aside several efforts by Mitchell and Jessen to dismiss the case. He repeatedly rejected their arguments that what constitutes torture is a political question, and admonished both sides not to use the upcoming trial to litigate the charged debate about post-9/11 interrogation policy.