The Chancellor and Work and Pensions Secretary insisted they would tackle the "damaging culture of welfare dependency" in a newspaper article which ended speculation the Conservatives might water down their election pledge to cut benefits so deeply.
Their comments were met with anger from Labour and the SNP.
The government's hardline stance is also expected to make Mr Osborne's emergency Budget on July 8 the focus of fresh anti-austerity protests.
Thousands took the streets at the weekend, with major demonstrations in Glasgow, Liverpool and London.
Mr Osborne and Mr Duncan Smith are understood to have reached agreement on £12billion of cuts which will be set out in the Budget and Autumn Statement later in the year.
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 which "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 previous coalition government shaved £21 billion off the welfare budget but Mr Osborne and Mr Duncan Smith warned it will still make up 12.7 per cent 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.
"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."
Labour leadership frontrunner Andy Burnham made clear he would oppose cuts to tax credits for people on low incomes, and reductions in benefits for the disabled.
He also insisted the Government's mandate for pushing through £12 billion of welfare cuts was "questionable".
Whilst accepting the need to bring Britain's deficit down, he said welfare cuts would have "some devastating consequences for individuals".
He added: "The country is not going to feel good, is it, if we get the deficit down but basically destroy our public services.
"I think this is pretty disgraceful what is going on today. Here we have a Chancellor that is frightening people, basically.
The SNP's social justice and welfare spokeswoman Eilidh Whiteford said: "The Tories have shown time and time again that they simply cannot be trusted on welfare.
"Their heartless cuts are hitting the working poor and vulnerable in our society hardest, including disabled people.
"Scotland can't afford these cuts.
"We need powers over social security in Scotland to allow us to protect, support and empower people who need help, rather than pushing them into poverty with punitive cuts and unfair sanctions as the Tories are continuing to do."
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