The commission recommends that local authorities should have full control of the whole range of property taxes, including council tax, and the freedom to set these in ways that suit local circumstances.
The report called for at least 50% of income to be raised locally as it was 50 years ago, though it has dropped to 18% today.
The Commission on Strengthening Local Democracy said giving local communities the democratic power to look after their own financial affairs is "fundamental" to local democratic choices and participation, and can also help the economy.
It said local people should decide on levels of local taxation in relation to the services they want and local governments should be able to set and raise new taxes to meet the needs of the community.
The report calls for a "re-imagining" of local government in Scotland, which it says is one of the most centralised countries in Europe.
It described the transition from more than 200 local councils in 1974 to only 32 "local" councils in 1996 as "one of the most radical programmes of delocalisation that we can identify anywhere in the world".
The report also calls for a fundamental review of the structure, boundaries, functions and democratic arrangements for all local governance in Scotland.
It said this review should be undertaken jointly by the Scottish Government and local government and should be based on principles such as strengthening local democratic accountability.
The independent commission spent a year intensively gathering evidence to produce the report.
Councillor David O'Neill, chair of the commission, said: "Over the decades Scotland has become perhaps one of the most centralised countries in Europe. We have built that view based on an open conversation over the last year with thousands of people across Scotland, the UK and Europe, and all of our evidence is publicly available. It is little wonder that many have lost faith in the democratic system altogether.
"Today, the argument is no longer about whether Scotland is out of step with other modern democracies. Instead, it is between those who think that this is acceptable, and those who believe that it must change. The question is about what democracy should be like in the years to come.
"Regardless of the outcome, are we prepared to let the referendum perpetuate old ways of thinking? In this report, we argue that it is time to take a much bolder step towards giving communities real choices, and putting the future into their hands."
The report also suggests creating more councils to give local people more powers.
It proposes various models such as a single-tier system with a much larger number of smaller local governments responsible for all services that can be governed, planned and delivered at local level.
Another option is a two-tier system where there are 32 councils with another tier of 150-200 community governments with responsibility for local community services.
The commission called for change whatever the outcome of the independence referendum on September 18.
It said: "The weak state of local democracy has come into focus as Scotland debates its future, and as one part of that debate draws to a close, we believe that it is the right time for another phase to begin.
"Regardless of the outcome of the referendum this September, Scotland can decide that it is time for a new kind of democracy and start to change now."