The Prime Minister kick-started the initiative by announcing that community projects in four parts of the country will get support from civil servants.
He insisted the scheme was about engaging people rather than offloading the state's responsibilities to the voluntary sector to save money.
But charities, unions, and Labour politicians raised doubts about how the plans would be funded while budgets were being slashed.
Communities Secretary Eric Pickles also risked contradicting his boss by saying the Big Society was "unashamedly about getting more for less".
Mr Cameron used a speech in Liverpool - one of the areas to benefit from state support - to hail the scheme's potential for shifting power from the state to individuals.
The other three areas picked to receive initial help with projects are Eden Valley, Cumbria; Windsor and Maidenhead, Berkshire; and the London Borough of Sutton.
Each will get an expert organiser and dedicated civil servants to ensure "people power" initiatives get off the ground and inspire a wider change, the Prime Minister said.
A local buy-out of a rural pub, efforts to recruit volunteers to keep museums open and giving residents more power over council spending are among the initiatives being championed.
Mr Cameron also confirmed plans to use funds stuck in dormant bank accounts to enable charities, social enterprises and voluntary groups to take over the running of public services.
Hundreds of millions of pounds should eventually be available in start-up funding as part of the push - which would see providers paid by results.
Mr Cameron said years of top-down government control had turned capable people into "passive recipients of state help", lively communities into "dull soulless clones" and motivated public sector workers into "disillusioned weary puppets of government targets".
Government had to be turned "completely on its head" to foster "communities with oomph", public sector workers with freedom to innovate and "a new culture of voluntarism, philanthropy, social action".
"These four vanguard communities will be the great training grounds of this change, the first territory on which real and ultra local power is a reality - and the Big Society is built," he added.
The Big Society Bank is based on legislation passed by Labour allowing money untouched for 15 years to be diverted to good causes if account holders cannot be traced by banks.
Ministers hope it will be operational quickly enough to see the first money distributed to groups by April next year.
Speaking on BBC Breakfast ahead of his speech, the PM denied that the Big Society concept of people taking on more responsibility was merely a way of masking public service cuts.
"It is not a cover for anything," he said. "I was talking about the Big Society and encouraging volunteering, encouraging social enterprises, voluntary groups to do more to make our society stronger, I was talking about that way before we had a problem with cuts and deficits and all the rest of it.
"This would be a great agenda whether we were having to cut public spending or whether we were increasing public spending."
He added: "This is not about trying to save money, it is about trying to have a bigger, better society."
Mr Pickles told BBC Radio 4's World at One: "Even at a time when money is tight it is still possible to find different ways of delivering.
"It is unashamedly about getting more for less. But it is about passing power down to folks so you can start to mould your own neighbourhood and put something back in."
Labour leadership contender Ed Miliband said Mr Cameron's declared commitment to the voluntary sector was belied by the cutbacks in Government support.
"The problem with what he is saying today is it comes at the same time as there are very big cuts in funding to the voluntary sector," he told the BBC.
"This is essentially a 19th century or US-style view of our welfare state which is cut back the welfare state and somehow civic society will thrive. That is the reality."
The chief executive of the National Council for Voluntary Organisations, Sir Stuart Etherington, said it was good Mr Cameron was "recognising the importance of the voluntary and community sector".
"However I am very concerned about the tidal wave of cuts about to hit the sector," he said. "These cuts will have a detrimental effect on the services received by some of the most vulnerable people in our society."
Dave Prentis, general secretary of the union Unison, said: "Cameron's Big Society should be renamed the big cop-out.
"The Government is simply washing its hands of providing decent public services and using volunteers as a cut-price alternative.
Mr Cameron hopes putting flesh on the bones of the Big Society philosophy - which he described as his "great passion" - will help it resonate with the public.
Despite putting the idea at the centre of the Tory election campaign, a recent poll found more than a third of voters were unaware of it - although many approved when it was explained to them.
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