Castlebeck, which runs Winterbourne View in Hambrook, Bristol, confirmed that the hospital would shut down on June 24, and the patients transferred to alternative facilities.
For the edition of Panorama aired on May 31, patients were secretly filmed at the hospital by an undercover reporter. The footage showed residents being slapped, taunted and pinned down.
A spokesman for the County Durham-based Castlebeck said that the company had been working with the NHS and social services to ensure patients were safely transferred to other facilities.
He said: "The hospital will effectively close this Friday when the last patients are transferred to alternative services.
"Castlebeck has been working closely with families and carers, commissioners and other professionals from the NHS and social services to ensure patients are safely transferred with minimum disruption to their lives."
After Panorama was broadcast, a number of people at Winterbourne View were questioned by police and the government said that it would carry out a review of what happened.
Castlebeck also commissioned consultancy firm PricewaterhouseCoopers (PwC) to undertake an independent review of the entire company.
In a statement after the programme was aired, Castlebeck chief executive Lee Reed said that he was "shocked, disgusted and ashamed" by what he saw.
"Having spent my entire career in health and social care, I intend to leave no stone unturned to ensure that this type of horrific event is never allowed to happen again", he said.
"I have been chief executive since January, and my priority is the patients under our care. My job now is to ensure that this company moves forward from this appalling episode to having among the best, if not the very best, standards in the provision of care for some of the most vulnerable people in society."
The BBC Trust recently cleared a Panorama documentary about the Israeli boarding of a boat in the Gaza flotilla.