An immediate inquiry is to be held into current and historical child sexual abuse in Telford.
A Sunday Mirror article last month claimed 1,000 children may have been abused in the town since the 1980s.
Until Saturday, senior councillors had called for the government to take the lead on any investigation.
But now Labour councillors have backed a motion by the opposition Conservative group in a unanimous decision to set up an independent, council-led inquiry.
At the weekend, council leader Shaun Davies said he had come to the conclusion a "council inquiry is better than none", however a council inquiry would only go ahead if the national inquiry into child sexual exploitation (CSE), the Jay Inquiry, decided not to investigate Telford.
Conservative opposition councillors said they were "extremely concerned" about any delay to an investigation.
Calling for an immediate inquiry, Conservative councillor Andrew Eade said: "I do hope we have an opportunity to do the right thing and unite this divided council".
A statement on behalf of the victims, read by Conservative councillor Nicola Lowery, said: "We deserve answers, our families deserve answers, answers the national inquiry will take years to deliver.
"The inquiry needs to start now. Things need to change. We want to be part of that change."
Mr Davies and other senior councillors had previously said a government-led inquiry would have have greater powers to gather evidence and would be perceived as more independent.
However, the proposal was swiftly rejected by the Home Office last month.
Standing in for Mr Davies, who could not attend Tuesday's council meeting due to illness, Labour councillor Lee Carter said the council is "going to move very quickly".
"This town is hurting," he said. "We've got to do everything we can to put this right."
Conservative MP for Telford Lucy Allan said she was "delighted" there will be an inquiry and the authorities have "a real opportunity to communicate to victims that they were not at fault, they have nothing to be ashamed of, and they can now come forward".
She said there had been a lot of "wriggling" and "squirming" from the Labour-run council in bringing an inquiry and suggested Mr Davies should stand aside as council leader.
"If I was him that's what I'd do," she said.
The council last published a review into child sexual exploitation in the town in 2016 following the jailing of seven men in 2012 as part of West Mercia Police's Operation Chalice.
The report concluded it was "clear that CSE is still taking place in Telford and Wrekin, although the true scale of this crime is unknown".
The year before, Telford and Wrekin recorded more child sex offences per capita than anywhere else in England and Wales, according to Home Office figures.
How to report child sexual exploitation
If you're worried that a child or young person is at risk or is being abused you can contact the children's social care team at their local council. You can choose not to give your details.
You can report it online to the Child Exploitation and Online Protection command (CEOP).
Or you can call the NSPCC 24-hour helpline on 0808 800 5000 for expert advice and support.
If a child is at immediate risk call 999, or call the police on 101 if you think a crime has been committed.
Children and young people can call Childline free on 0800 1111 where trained counsellors are available 24 hours a day, every day.