The chancellor said he had found 20% of the £11.5bn he wants to cut spending by in the year from April 2015.
Justice, energy and communities are among the departments agreeing to “significant savings”, he said, adding that health, schools and foreign aid would be protected from cuts, reports The BBC.
The opposition is expected to say the government has cut too much too fast.
Mr Osborne told the BBC that no chancellor had got so far in agreeing so many plans so far ahead of a spending review – which is due towards the end of June.
The departments which have agreed to make cuts of between 8% and 10% are: Ministry of Justice, the Department for Communities and Local Government, the Department for Energy and Climate Change, The Treasury, the Cabinet Office, the Foreign Office and the Northern Ireland department.
Mr Osborne said the scale of the savings expected were “difficult” but necessary to reduce government borrowing and to ensure money could be found to spend on the “nation’s priorities” such as the health service.
“The fact we have got big departments like the Ministry of Justice signed up to 10% reductions shows we are on track and there is a cabinet will behind delivering these necessary savings,” Mr Osborne told Radio 4’s Today programme.
Negotiations over savings are continuing with other big departments, such as the Ministry of Defence and the Home Office, but ministers have insisted they he would not do anything to put at risk people’s safety “at home or abroad”.
The financial details will be held back until the review is presented to Parliament next month.
But it is understood that taken together the savings agreed so far in talks with departments and in previous announcements mean the Treasury still has to find £8bn of the £11.5bn to be saved in the spending review.
There have been reports some ministers – such as Defence Secretary Philip Hammond – are unhappy about the scale of cuts but Mr Osborne said all his colleagues accepted the need for them and he was “confident” they could be achieved.
Mr Osborne rejected suggestions that the criminal justice system would be undermined by the cuts, saying major reforms were also under way to make the courts and probation services more efficient.
The government, he added, was “trying to improve the quality and productivity of public services while making sure we are not wasting money” and Whitehall “could not be let off the hook” in the push for more efficient government.
He also suggested that there would be no further cuts in welfare in the year in question on top of the “substantial” ones already announced.
Earlier this month, the Commons Public Accounts Committee warned the UK may not be able to afford projected levels of spending on military equipment over the next decade.
Its report was based on a government pledge for a 1% increase in defence spending in the review, and in following years.
