It is part of the Government's "Big Society" agenda, which will see community projects in four parts of the country given help in a bid boost "people power" and inspire change.
The 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. Ministers hope it will be operational quickly enough to see the first money distributed to groups by April next year.
The Prime Minister said last month he wanted an increase in community work and social enterprise to be one of the coalition's "great legacies".
Other elements include a National Citizen Service for 16-year-olds and a US-style "neighbourhood army" to encourage involvement.
Mr Cameron will be making a speech in Liverpool today, one of the four areas to benefit from targeted help, to unveil the initiative.
"The Big Society is about a huge culture change where people, in their everyday lives, in their homes, in their neighbourhoods, in their workplace, don't always turn to officials, local authorities or central government for answers to the problems they face, but instead feel both free and powerful enough to help themselves and their own communities," he will say.
"It's about people setting up great new schools, businesses helping people getting trained for work, charities working to rehabilitate offenders."