The group, which is to be chaired by former party leader Iain Duncan Smith MP, will "develop ideas to empower the voluntary sector, foster social enterprise, increase the scope of community action and encourage neighbourhood revival".
Announcing the initiative at the Eastside Young Leaders Academy in Plaistow, east London last week, Cameron said the group would also study the causes and consequences of poverty in Britain.
He added that it would develop "practical ideas to empower the least well off to climb the ladder from poverty to wealth".
Debbie Scott, chief executive of Tomorrow's People, will act as deputy chair of the project, which will receive the input of two Conservative MPs and eight advisers "from outside politics".
Scott said: "We are looking forward to being part of this commission, drawing on our own 21 years of experience in helping people out of long-term unemployment, welfare dependence and homelessness, and into jobs and self-sufficiency."
The social action group, named on its website as the Social Justice Challenge, will look at policy areas including care of elderly and disabled people, drug dependency and alcohol abuse.
"It will examine the challenges facing young people and their parents, focusing on family policy, parenting and childcare, support during the early years and barriers to the fulfilment of teenage aspiration," Cameron explained.
Also announced last week was the new Quality of Life policy group, which will draw on the expertise of environmental charities in an attempt to shift the green agenda to centre stage.
Cameron wants the group, which will be "radical in its thinking", to take evidence from leading NGOs including Friends of the Earth and Greenpeace.
The group's remit will be to explore solutions to climate change, pollution, traffic-choked streets and blighted urban landscapes.
- See Nick Cater, page 26
- The new Conservative leader, David Cameron, has launched a social action group looking into how to achieve social justice
- The group will "empower the voluntary sector, foster social enterprise and increase the scope of community action"
- Debbie Scott, chief executive of Tomorrow's People, will act as deputy chair to Iain Duncan Smith.