However, the price will be more cuts to UK Government departmental budgets, which are likely to result in hundreds, if not thousands, of civil service job losses, some falling in Scotland.
The extra capital investment was "very good news for Scotland", a senior Treasury source told The Herald. The source added: "There will be full Barnett consequentials from this."
Under the Barnett formula, the Scottish Government will receive a proportion, roughly 10%, of extra spending by Whitehall. Equally, however, cuts to budgets will be reflected in how much money Scotland receives.
The reductions in Whitehall departmental budgets will save £1bn in 2013/14 and £2.5bn in 2014/15.
Just where the remaining £1.5bn will come from will, said the Treasury source, be revealed by the Chancellor this afternoon in his statement to MPs.
The source stressed that, while the cut to Whitehall departments would be 1% next year and 2% the year after, because the large budgets of health and education were being protected, the proportionate impact on Scotland would be much smaller – 0.2% in 2013/14 and 0.4% in 2014/15.
The decision to boost capital spending and cut departmental budgets was relayed by Mr Osborne at yesterday's weekly Cabinet meeting.
Yesterday, Prime Minister David Cameron said: "Government departments aren't actually spending up to their budgets.
"We can say to them 'you've got to cut back some spending, including some unnecessary spending and let's put that money into things that will make a difference in our country and in our economy – more roads, more school buildings, more infrastructure to make our economy work better, to make our country work better'."
The PM's spokesman made clear the spending rises and cuts proposals would be within the overall fiscal plan and would not involve extra borrowing.
He explained they would "in part" be funded by reductions in departmental budgets but also declined to say where the other part would come from. The spokesman stressed that current commitments would be maintained, such as health spending, and frontline services would be protected.
He pointed out how an internal review had shown how many departments were "over-achieving" on efficiencies, currently underspending to an average of £3bn a year, and further efficiencies could be made.
The spokesman referred to the Department for Education and its administrative cuts. Secretary of State Michael Gove sparked controversy by announcing departmental job cuts of 1000, one-quarter of the workforce.
Asked if budget reductions would result in similar job losses, the PM's spokesman replied: "We certainly want to deal with administrative budgets."
He said the extra capital funding would be channelled mainly into transport, schools, skills and science. For example, £1bn will be invested in new schools with around 100 new academies and free schools will be built in England.
The Herald was later told the departmental budgets of HM Revenue and Customs, local government and international development would be exempted.
The Ministry of Defence will be given additional flexibility to roll over underspends, which last year amounted to almost £400m, from one year to the next. As a result, ministers believe there will be no reduction in military manpower and core MoD budgets. Nuclear decommissioning will also be protected.
This means the departments looking at the deepest cuts include the largest spender, the Department for Work and Pensions, the Home Office, the Department for Energy and the Department for Culture, Media and Sport.
No 10 stressed the extra spending meant the Coalition would deliver higher levels of annual capital investment, as a proportion of GDP, than under recent Labour administrations.
However, Rachel Reeves, the Shadow Chief Secretary to the Treasury, said the Chancellor seemed to have finally admitted his deep cuts to infrastructure investment were a "catastrophic mistake which cost jobs and weakened our economy".
She said the extra funding for new free schools in England would be smaller than the huge cuts he made two years ago to school and college buildings.
Ms Reeves added: "George Osborne must explain which frontline services, like the police and social care, he will cut further to pay for this latest U-turn."