Government spending on consultants would be cut by half and communication spending by a quarter - saving £650m - while more Civil Service staff would be relocated from London to "cheaper" premises.
Whitehall departments could set up "common spending policies" and share office space, as part of a "third generation of changes in public services".
In its report, Putting The Frontline First, the government points out there are now 4,300 senior civil servants compared with 3,100 in the mid-1990s.
Mr Brown said public sector workers earning an "over-generous" salary would be "named and shamed", as many had "lost touch" with normality.
In future, all new public sector jobs with salaries above £150,000 will have to be approved by the Treasury while the details of civil servants and other public sector managers under direct ministerial control currently earning that amount will be published.
Mr Brown has ordered a review of senior public sector pay by the Senior Salaries Review Body to report by the Spring.
He said: "Money which should be spent on health, on schools, on policing and on social services is, in some cases, going on excessive salaries and unjustified bonuses, far beyond the expectation of the majority of workers.
"This culture of excess must change and will change."
He added that the government would use technological advances to make services more user-friendly and cheaper.
As an example, sending text messages to remind patients about GP appointments could help save up to £600m a year wasted on missed visits.
The public needed more "feedback and interaction" when using services, such as crime maps and giving parents online details of children's progress at school, he added.
'Further than before'
Mr Brown promised to bring more such details on to the internet by next year.
"The proposals we are setting out in this plan - which is just one element of our efforts to reduce the deficit - will go further than we have ever gone before in streamlining central government," Mr Brown said.
The hard truth is that, even if implemented, you will never be sure that any of these measures saved the government cash
"We have already promised savings of £35bn a year by 2011 on top of the £26.5bn a year already delivered through the Gershon [spending] review.
"But by identifying new ways of working - and being prepared to make the tough choices - we can deliver in excess of another £12bn in efficiency savings over the next four years.
"This includes £3bn of new efficiency savings identified since the Budget - of which over £1.3bn will come from streamlining central government."
The proposals were laid out in Parliament by Liam Byrne, Chief Secretary to the Treasury, who said that saving money should be "everybody's business".
Chancellor Alistair Darling told BBC One's Andrew Marr show on Sunday that public spending would be "a lot tighter than it was in the past" as a result.
He said parts of the troubled £12bn NHS IT system would be delayed as it "isn't essential to the front line" - a move Health Secretary Andy Burnham told MPs on Monday would save £600m "over the lifetime of the programme".
Mr Darling said the full details of spending cuts would not be revealed until "the first half of next year at some point".
Greater efficiency is always welcome, but we will not get the improvements we need until there is fundamental reform in Whitehall
Jeremy Browne Lib Dem spokesman
Meanwhile, as part of plans to tackle the deficit in public finances, the Treasury is working on a possible windfall tax on what it sees as the exceptional profits of banks or the excessive bonuses of bankers.
But the Conservatives say the government is still not revealing the full extent of cuts needed to tackle Britain's debts.
They say they would protect NHS and international development spending but the rest of Whitehall would face "very difficult choices" if the Tories won power.
The party has also called for a moratorium on all government computer projects, claiming Labour has spent £100bn on IT since 1997 and that contracts worth another £70bn are due to be renewed or commissioned in the next two years.
Shadow Treasury minister Philip Hammond told MPs: "Since 2000 they've poured billions of pounds of taxpayers' money into indifferent public services, borrowing and spending like it's Monopoly money."
He called Labour's savings plans a "mish-mash of announcements and stolen clothes, in the dying months of their rule".
Liberal Democrat Treasury spokesman Vince Cable said: "If the government knew there was inefficiency, why hasn't the government already dealt with it?"
We have now reached the point where the investment gap which we inherited...in 1997 has been fixed
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