The Hill End Compensation Scheme will compensate anyone who suffered abuse at the facility between 1969 and 1995.
A three-year long police investigation found that young people were physically and sexually abused at the Hill End Hospital over a period of two-and-a-half decades.
"It is a recognition that what we went through as children happened, that it was wrong and that it has caused unimaginable damage. When we were children, we had no voice.
Senior solicitor Saoirse Kerrigan led the negotiations for the firm.
She said: “The descriptions our clients have provided of Hill End Adolescent Unit are of a brutal and dark place.
"The evidence we have seen shows that for many years children who went through the unit were routinely sedated as a form of punishment and control, often rendering them unconscious and vulnerable to abuse, and leaving them traumatised for many years to come.