The group, which will meet for the first time next Wednesday, is led by LGA chief executive Paul Coen and CBI director of public services Neil Bentley.
The CBI said the meeting will be the first time members are formally brought together to discuss ways to increase efficiency.
The two bodies said the group would increase the chances of achieving practical solutions on issues such as driving down bid costs and improving councils’ commissioning and procurement skills.
While it is not known which CBI members will participate, it is likely that those on its local government panel, such as Accord, Amey, HBS and Vertex, will be included.
A joint letter sent by Mr Coen and Mr Bentley to senior figures in the public and private sectors said: “We are proposing to undertake detailed work on new models of service delivery and examine what is needed to influence behaviours and improve skills across all sectors.
“We see this high-level working group as the core leadership group for the wider local government and supplier communities.”