Welfare cuts worth £12bn a year will be announced in next month's Budget, after the Government agreed "significant" spending reductions in the last few days.
On a weekend during which tens of thousands of protesters marched against austerity , Chancellor George Osborne and Work and Pensions Secretary Iain Duncan Smith signalled they would press ahead with cuts.
The welfare changes will include capping benefits at £23,000 a year for each family. Cuts to housing benefit and tax credits are also expected, defying speculation the promised cuts to the welfare budget would be watered down.
In an article in the Sunday Times, the joint letter from Mr Osborne and Mr Duncan Smith wrote: "This government was elected with a mandate to implement further savings from the £220bn welfare budget.
"For a start, we will reduce the benefit cap, and have made clear that we believe we need to make significant savings from other working-age benefits.
"We will set out in detail all the steps we will take to bring about savings totalling £12bn a year in next month's Budget and at the spending review in the autumn.
"It took many years for welfare spending to spiral so far out of control, and it's a project of a decade or more to return the system to sanity.
"Reforming the damaging culture of welfare dependency and ensuring that work pays has been central to our mission to make Britain fit for the future."
The planned cuts emerged as anti-austerity protesters demanded an end to government cuts.
Organisers estimated that 250,000 people took part in the demonstrations in London, Glasgow, Liverpool and Bristol, including celebrities Russell Brand and Charlotte Church.
The decision to write the article on the same weekend as the protests will be seen as deliberately provocative.
The two ministers wrote: "All our reforms will have these central aims: to ensure the welfare system promotes work and personal responsibility, while putting expenditure on a sustainable footing.
"Welfare reform is fundamentally about opportunity and changing lives, supporting families to move from dependence to independence - a vital point, because without social mobility there can be no social justice."
Andy Burnham, Labour leadership candidate and shadow health secretary, said: "I think this is pretty disgraceful, what is going on today.
"Here we have a chancellor that is frightening people basically ... just waving around this idea of huge cuts drastic cuts, without spelling out where they are going to come from.
"He did not spell it out before the election, and he is still not spelling it out now. This is just not acceptable.
"He is trying to play politics by challenging us, but actually in doing that he is frightening vulnerable people. And that is wrong."