The department will carry out an investigation into how the late DJ and broadcaster was appointed to the taskforce to reform patient care in a hospital which houses some of the country's most notorious criminals.
Lawyer Liz Dux, who is acting for some victims and preparing legal action against the BBC and Stoke Mandeville hospital – where Savile is also said to have carried out sexual assaults – said it was possible the government could also face civil claims, as it was directly responsible for the running of the Broadmoor high-security psychiatric hospital in that time.
Ken Clarke, currently a Cabinet minister without portfolio, was Health Secretary when Savile was appointed in 1988. He said: "I have no recollection of ever having met Jimmy Savile and no recollection of these events. The DoH are rightly now investigating to establish the facts."
In a statement, the department said: "We will investigate the Department of Health's conduct in apparently appointing Savile to this role.
"Although the framework for child protection and safeguarding for Broadmoor and other special hospital patients changed radically in 1999, we of course want to establish the circumstances and see if any lessons can be learned.
"In hindsight he should very obviously not have been appointed. Had anyone involved in the appointment been aware of allegations of abuse against Savile, we would not have expected him to have been appointed."
Allegations have been made that Savile abused a 17-year-old patient during a visit to the psychiatric hospital in Berkshire as a fundraiser in the 1970s. The DoH described the abuse claims as "disturbing". In Broadmoor, Savile had an office, a bedroom and his own set of keys to wards.
Broadmoor is the latest publicly funded body to be embroiled in the scandal. The BBC is under mounting pressure over revelations that Newsnight abandoned an investigation into Savile, that the TV presenter assaulted children in his dressing room, and that staff were aware of the Jim'll Fix It presenter's behaviour and failed to take action.
The ITV documentary on Savile which sparked the scandal and featured five women alleging he abused them also included claims that he targeted young hospital patients at Stoke Mandeville in Buckinghamshire and Leeds General Infirmary.
Childline founder Esther Rantzen was also dragged into the controversy yesterday when it was claimed she had been told of rumours about Savile 18 years ago by abuse campaigner Shy Keenan.
But the veteran broadcaster said she could not recall a conversation with Keenan and that, while she heard rumours about Savile's behaviour, she never heard or saw any evidence, and would have acted upon it if she had.
Rantzen said: "I don't mean any disrespect to the lady but I don't remember any conversation with her. I have had a great many conversations with people over the years and whenever possible I have investigated what people told me and told the police and social services.
"I never heard anything from a child or from anyone who worked with him. The rumours I heard were from people who never met him and they could have easily been as false as they were true. If we had any sort of evidence we would have reported it immediately to the police. Nobody I know would have dreamed of covering up this crime.
"The lady ... only had rumours to go on. She did not have any evidence. I hope if she did have evidence that rather than telling me she would tell the authorities."
BBC director-general George Entwistle has offered a "profound and heartfelt apology" to the alleged victims of Jimmy Savile's sexual abuse as he announced that two inquiries would be launched.
One will look into whether there were any failings over the handling of an abandoned Newsnight investigation into Savile. A second independent inquiry will look into the "culture and practices of the BBC during the years Jimmy Savile worked here".
Entwistle said: "As the director-general of the BBC I have made clear my revulsion at the thought that these criminal assaults were carried out by someone employed by the BBC and that some may have happened on BBC premises as well as, we now discover, in hospitals and other institutions across the UK.
"I have one thing to repeat – that is a profound and heartfelt apology on behalf of the BBC to every victim. It is the victims, these women who were subject to criminal actions, who must be central in our thoughts."
Scotland Yard is pursuing 340 lines of inquiry in the Savile abuse case involving 40 potential victims. So far 12 allegations of sexual offences have been officially recorded but this number is increasing, police said.
Metropolitan Police detectives are in contact with 14 other forces as the number of allegations against the former DJ continues to rise.
Details of two allegations have been passed by Scottish police to the Metropolitan Police which is leading the investigation.
Tayside Police confirmed they had made a second disclosure about a "historical incident". A Tayside Police spokesman said: "Full details are still to be established, however, information has been provided to the Metropolitan Police regarding it." Earlier, the force passed on details of another incident said to have taken place in Liverpool.