George Osborne and Iain Duncan Smith are to go ahead with plans to slash another £12 billion a year from the benefits bill.
The Chancellor and Work and Pensions Secretary reiterated their determination to achieve the savings in full as a huge anti-austerity protest brought nearly 250,000 demonstrators out onto the streets of London.
The two men are believed to have thrashed out details of the cuts pledged in the Tory manifesto over the last few days - putting paid to rumours that they could be scaled back or delayed.
They have already said the household benefits cap will be reduced from £26,000 to £23,000 a year and housing benefit and tax credits are expected to bear the brunt.
However, David Cameron has pledged full protection for child benefit and pensioner benefits.
Writing in the Sunday Times, Mr Osborne and Mr Duncan Smith insisted they had inherited a "crackers" welfare system from Labour in 2010.
Repeating the claim that Britain makes up 7% of all the welfare spending globally despite having just 4% of GDP, the pair said the arrangements had "incentivised people to live a life on benefits".
They argued that the new universal credit would rationalise the "Byzantine" network of means-tested payments and ensure it is always in the interests of those on benefits to work more.
The coalition shaved £21 billion off the welfare budget, but Mr Osborne and Mr Duncan Smith warned that it will still make up 12.7% of spending in 2019-20.
"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," they wrote.
"This government was elected with a mandate to implement further savings from the £220 billion 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 £12 billion a year in next month's Budget and at the spending review in the autumn.
"As before, 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. It is the right thing to do."
Tens of thousands of protesters took to the streets of London, lighting fires and throwing smoke bombs as they demanded an end to the government's austerity programme.
The crowd was addressed by left-wing comedian Russell Brand and singer Charlotte Church among others.