Trouble-shooters will be sent in to turn around 120,000 "deeply damaged and broken" families under a £448 million plan announced by David Cameron.
The Prime Minister said the current bill for dealing with each chaotic household was around £75,000 on average - a total of £9 billion a year.
In a speech to charities, he claimed the troubled families programme would "save the country a fortune" as well as rebuild "shattered" lives. Councils will have to put up 60% of the cash needed for the plans and the Government will stump up the remaining 40%.
Critics claimed that local authorities would struggle to find the money at a time of swingeing budget cuts and raised "deep concerns" that the Government's contribution would be funded by reductions in other areas.
Mr Cameron said he wanted to reform the system that means a "string of well-meaning, disconnected officials" treat the "symptoms and not the causes" in difficult families. Instead, there will be a "clear hard-headed recognition" of where families are going wrong.
He added: "We are basing this on what works. There are local councils around this country that have got programmes that are fixing the broken families. Let's make sure we do that right across the country - we'll save the country a fortune but at the same time we can help rebuild what are very broken and shattered lives.
"This immense task will take new ways of thinking, committed local action, flexibility and perseverance. But I know too that it's a task we can't shirk. People in troubled families aren't worthless or pre-programmed to fail. I won't allow them to be written off.
Mr Cameron first pledged to "turn round every troubled family in the country" by the end of the current Parliament last year. But he admitted the summer riots "were a wake-up call" and "not a freak incident but a boiling over of problems that had been simmering for years".
The trouble-shooters will be responsible for identifying problem households and getting family case workers involved.
Gloria De Piero, shadow Home Office minister, said: "Expecting cash-strapped local authorities to provide 60% of the funding for new projects seems unrealistic when ring-fences have been removed and local services are already being closed down."
