A public inquiry will investigate allegations of mistreatment at G4S-run Brook House immigration removal centre.
Alleged abuse of detainees at the centre near Gatwick Airport were filmed by an undercover BBC reporter in 2017.
An ongoing probe by the Prisons and Probation Ombudsman (PPO) will now have the power to compel witnesses to give evidence, the Home Secretary said.
G4S said it would "co-operate fully with the inquiry," adding that Brook House detainees were "well treated".
Panorama footage aired in September 2017 showed alleged assaults, humiliation and verbal abuse of detainees by officers at the centre.
At least six staff members were dismissed by G4S.
Home Secretary Priti Patel said: "I want to establish the facts of what took place at Brook House and ensure that lessons are learnt to prevent these shocking events happening again."
Lawyers for two former detainees had argued at the High Court that only a public inquiry would be able to make sure witnesses give evidence and provide "accountability and lesson-learning".
A High Court judge ruled in their favour in August and the Home Office failed in a bid to challenge the ruling.
Ms Patel said the inquiry, which should reach its conclusions within 12 months, will identify whether there was any mistreatment and who was responsible.
It will also look at whether the actions or policies of the Home Office and its contractors "caused or contributed to any identified mistreatment" and whether any changes would prevent mistreatment in the future.
It will not determine the civil or criminal liability of any people or organisations involved, she said in a ministerial statement.
John Whitwam, of G4S, said: "We are focused on the continuous improvement of Brook House IRC.
"The latest inspection was positive, with HM Chief Inspector of Prisons commenting that the centre is safe, detainees are well treated and there is a positive culture of proactive leadership."