The study from the UK's Changing Union body, a research partnership looking at devolution from a mainly Welsh perspective, called for new arrangements to represent BBC viewers in Scotland, Wales and Northern Ireland.
It called for existing audience councils to scrapped and replacement by three National Broadcasting Trusts operating with their own budgets under the umbrella of the BBC Trust.
It also called for the devolved administration in Wales and Northern Ireland to appoint BBC Trust members jointly with UK ministers, bringing them into line with Scotland.
The three administrations should also appoint representatives directly to Ofcom, the broadcasting regulator, the report said. It said local and community radio should be licenced by Ofcom committees in Scotland, Wales and Northern Ireland.
The UK's Changing Union is a project run by the Wales Governance Centre at Cardiff University, the Institute of Welsh Affairs and Tomorrow's Wales, an independent think-tank.
Director of the Wales Governance Centre Professor Richard Wyn Jones said: "In the post-devolution era, it is no exaggeration to say that the democratic health of the smaller nations of the UK depends on a properly functioning and resourced public broadcasting system.
"Yet so far there has been little or no attempt to adjust the way that public broadcasting in the UK is governed in order to reflect the new realities. These proposals would give the devolved level a voice in key decisions whilst retaining robust UK-wide structures and are thus wholly in keeping with the spirit of devolution."
The Scottish Government plans to create a Scottish Broadcasting Service, based on the assets and staff of BBC Scotland, if the country becomes independent.
It hopes the new national broadcaster would form a joint venture with the BBC to retain the full range of programmes and services.