The ability to take decisions at regional level would benefit local economies, he said.
Mr Straw said Labour's commitment was clear in its draft manifesto, New Labour, New Life for Britain.
'As a first stage, there will be regional chambers, indirectly elected bodies of existing councillors. As a second stage, in those regions where there is a clear popular consent expressed through a referendum or other means, directly elected regional assemblies can be established alongside a predominantly unitary system of local government.
'Across Britain, people want a greater say in the decisions that affect them,' he said.
'They know that many decisions have to be made by national government. But they also want many other decisions to be taken at a regional or local level, and resent the increasing central domination and control over the regions and localities of England that we have witnessed over the last decade and a half,' he said.
'The huge error made by the present Tory administration is their lack of understanding that people have loyalties which are complementary to each other. We can and should each be proud of being British, proud of our ties with one or other of the four historic nations which make up the UK, and proud, too, of our sense of identity which comes form our association with a region, city, town or village where we live or have our roots.
'Tory central government has viewed regional and local loyalties as a threat to its power in Whitehall - we need only look at the plethora of quangos 'parachuted in' to the north east and to the regions to see that.
'But such loyalties and the bonds that go with them have enormous potential to act as the engine for real economic and social regeneration to the benefit of the region and the country as a whole,' he said.
'We in the Labour Party are committed to decentralise Britain's government to make it more in tune with people's needs, closer and more accessible to them . . . In our view strong practical benefits will flow form decentralisation - in terms of the region's economy, its transport system, its future planning, and in people's sense of ownership of the communities in which they live,' he said.