Osborne and Treasury Chief Secretary Danny Alexander briefed Cabinet on the plan this morning, on the eve of a Budget in which the chancellor is coming under intense pressure to inject vigour into an economy teetering on the brink of a triple-dip recession.
Health, schools, overseas aid and HM Revenue and Customs will be shielded from the cuts, and local government and police budgets will be protected for the first year, but other Whitehall departments will be told to deliver 1% savings on their day-to-day budgets for each of the two years 2013/14 and 2014/15, on top of cuts from previous budgets and autumn statements, the Prime Minister's official spokesman said.
Osborne told Cabinet colleagues at this morning's weekly meeting in 10 Downing Street that the savings were made possible because departments have under-spent their budgets this year by more than the historical average, according to forecasts to be published alongside the Budget tomorrow.
The Chancellor has decided to take account of this under-spending when setting departmental budgets for the next two years, Cabinet was told.
The Ministry of Defence will be given special flexibility to roll over unspent money, which the Chancellor believes will more than compensate for the cumulative savings demanded from the department in December's Autumn Statement and tomorrow's Budget. And capital spending plans across Whitehall will not be affected.
But departments such as environment, energy, transport and justice will have to find the 1% annual savings to day-to-day "resource" budgets in full. In total, Osborne expects the change in spending plans to save the Treasury £2.5 billion over two years.
It is understood that the savings will be taken into account in Osborne's Spending Review for 2015/16, to be unveiled in June, delivering around £1.2 billion of the £10 billion spending cuts which he is looking for in that year.
David Cameron's official spokesman told reporters at a regular daily press briefing that the underspends recorded this year "reflect the success that secretaries of state across the board have had, working with the Treasury, on bringing departmental resource spending down".
Total annual underspends across Whitehall departments have averaged around £6 billion since 2007. The forecast underspend for 2012/13, to be announced by the Office for Budget Responsibility tomorrow alongside Osborne's Budget, is expected to be "somewhat higher" than that figure, said the spokesman.
Cabinet ministers including Philip Hammond have recently gone public with concerns at the level of cuts their departments are likely to face in June's Spending Review.
But the PM's spokesman said Osborne's announcement today was greeted with "unanimous agreement around the Cabinet table that it was the right thing to do".
The permission granted to the MoD to roll over unspent cash is worth £1.6 billion to the department over the next two years - more than the total value of the 1% cut to its budgets in 2013/14 and 2014/15.
But devolved administrations will not be spared, as the 1% reductions will be reflected in the central Government funding arrangements for Scotland, Wales and Northern Ireland.
The Cabinet meeting also heard an update from Treasury minister Lord Deighton, who has been tasked with accelerating the delivery of major infrastructure projects, on progress in the Government's "Top 40" capital spending plans.
TUC general secretary Frances O'Grady said: "With the economy stagnating, the pressure is on the Chancellor to deliver a pro-growth Budget.
"But spending just £2.5 billion a year more on infrastructure projects will boost growth by a measly 0.06%. Worse still, funding it through departmental spending cuts will mean further reductions in public services.
"With interest rates negative in real terms, the Chancellor has the perfect opportunity to invest in Britain's future, rather than raiding departmental budgets to cover his failed economic strategy."