Shayan Badraie sued the department over his experiences in the Woomera and Villawood detention centres between 2000 and 2002.
His lawyer, Rebecca Gilsenan, from Maurice Blackburn Cashman says he has a psychiatric condition and symptoms which fluctuate.
The Department of Immigration has confirmed that a settlement has been reached and that the Badraie family has been granted Australian visas.
Visas for Australia
Ms Gilsenan says the settlement should assist Shayan's recovery, while the granting of visas should help the family to settle in Australia.
"The grant of the visa and the resolution of this case will allow this family to settle permanently and to have some certainty and to be able to try and look after their child and address the illness that he developed because of the way he was treated in immigration detention," Ms Gilsenan told ABC radio.
Ms Gilsenan says the deal has set a precedent for other detainees who may be in similar circumstances.
“The problems that Shayan experienced were systemic problems rather than ones that were just specific to him…” she said.
“So it’s quite possible that there are other children or even adults out there who lived in a similar environment during that time in immigration detention…. ” Ms Gilsenan added.