An inquiry will be launched into "systematic failures" that allowed Wayne Couzens to continue to be a police officer, Priti Patel announced.
The home secretary said the public "have a right to know" why he remained in the Metropolitan Police despite concerns about his behaviour.
Couzens kidnapped, raped and murdered Sarah Everard while he was a serving officer, using his police warrant card.
He has since been linked to allegations of indecent exposure.
The Met has faced mounting questions over its policies and procedures in the wake of Ms Everard's murder.
It was revealed Couzens - who worked as an armed officer in the Met's parliamentary and diplomatic protection team - was linked to several alleged incidents of indecent exposure, including in the days before Ms Everard's abduction in March.
Speaking at the Conservative Party conference in Manchester, Ms Patel said: "We need answers as to why this was allowed to happen.
"I can confirm today there will be an inquiry, to give the independent oversight needed, to ensure something like this can never happen again."
The Home Office said the inquiry would be in two parts, with the first examining Couzens' behaviour and establishing a definitive account of his conduct in the lead up to his conviction for Ms Everard's murder.
It said the second part would address specific issues, such as vetting procedures, standards, discipline and workplace behaviour.
The exact nature of the inquiry is still unclear.
The Home Office said it would initially be non-statutory but could be converted to a statutory one if required.
If statutory, the inquiry would have the legal power to call witnesses and limit the government's control over how it operated.
The person who would lead the inquiry and its terms of reference would be confirmed "in due course".
Policing minister Kit Malthouse pointed out the first option - a non-statutory inquiry - was much quicker to put in place but stressed it would not begin until the separate Independent Office for Police Conduct (IOPC) inquiry was complete.
On BBC Radio 4's PM, he acknowledged his surprise on finding out that examining social media postings had only became a part of the police vetting procedure a year ago.
The modern world was moving fast, he said. The vetting "net" has to be as tight as possible, with a regard for recruits' right to privacy while ensuring they were "the right people with the right values", he added.
Jamie Klingler, co-founder of the campaign group Reclaim These Streets, set up after Sarah Everard's murder, insisted the inquiry needed to be statutory and judge-led - and needed to include women.
"It seems really specific about Wayne Couzens and not about the system that allowed a Wayne Couzens to happen," she told the BBC.
"It's not admitting that there is systemic misogyny within the force that allowed this to happen, and by not doing so it's pushing it under the carpet rather than exposing [it] at all levels."
Couzens, 48, killed Ms Everard, 33, after stopping her on a street in Clapham, south London. He was sentenced to a whole-life prison term last week.
Speaking earlier, Prime Minister Boris Johnson said he did not support calls to make misogyny a hate crime, saying there was "abundant" existing legislation to tackle violence against women.
He told BBC Breakfast that "widening the scope" of what you ask the police to do would just increase the problem - but recruiting and promoting more female officers would help change the culture within forces.
Failure of the system?
There is an air of crisis in British policing as it faces a significant moment of reckoning.
Never have leaders felt that public trust is so low they have had to advise women to consider fleeing if they are uncomfortable when confronted by one of their own officers.
This is the aftershock of the appalling crimes of Wayne Couzens, who kidnapped, raped and murdered Sarah Everard while working for the Metropolitan Police.
Despite repeated attempts to force Home Secretary Priti Patel's hand, she has very publicly backed Met Commissioner Dame Cressida Dick by renewing her contract last month.
But questions now confront policing - and the difficulty its chiefs and ministers are having in answering them is why the crisis feels too deep.
Was Couzens' ability to pull on the uniform a failure of the system?
Is there a wider cultural problem?
And how should police leaders and the government respond?
Read more from Dominic here.
Met Police Commissioner Dame Cressida Dick, who has rejected calls to resign, confirmed on Monday there would be a separate independent review into the force's standards and culture.
Speaking to the BBC, Dame Cressida said Ms Everard's murder had made "everyone in the Met furious and we depend on public trust".
"In this country policing is done by consent and undoubtedly the killing of Sarah and other events has damaged public trust," she said, adding she was determined to rebuild it.
Labour's Yvette Cooper, chairwoman of the Commons Home Affairs Committee, said it was important the inquiry looked at how allegations of violence against women and girls were handled by police officers, as well as Couzens' conduct and the culture within the police.
Mayor of London Sadiq Khan said the inquiry "must leave no stone unturned" and should address reports of "widespread cultural issues".
Speaking earlier at the Conservative Party conference, Justice Secretary Dominic Raab said making communities safer and allowing women to walk home feeling safe at night was his "number one priority".
The Met Police said 650 more police officers would patrol hotspot areas in London over the next six months, with 150 of these working in local wards as "Bobbies on the beat".
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