The report also said that the idea of regulation in the mortgage market should be debated - but that it was too early to put forward specific action.
But it ruled out the separation of retail banking - banking for individuals and small firms - from the riskier business of investment banking.
The actions needed to implement the various recommendations and a timeline of when they are expected to be done are included in the report - although many of the key measures are described as at a time "to be determined".
The report followed the onset of the financial crisis which brought down several banks - including Northern Rock - and has left some of the world's biggest banks unable to survive without help from taxpayers.
"The changes recommended are profound, and the banking system of the future will be different from that of the last decade," Lord Turner said.
"The world's economy will be better served as a result," he added.
The chief executive of the British Bankers' Association, Angela Knight, said "financial regulation has to change here and around the world".
"The detailed discussions which will flow from this report are going to be vital as we need to ensure that the new framework is appropriate for small banks as well as the larger institutions and the UK retains it attractiveness for foreign banks," she added.
However the union, Unite, described the review as having "more rhetoric than substance", saying it would "do nothing to reassure consumers or staff in the financial services industry".
And Peter Vicary-Smith, chief executive of the consumers' association Which? said protecting consumers from rogue firms should be the FSA's top priority.
"The FSA must show it has real teeth by hitting companies with bigger fines, and naming and shaming offenders," he said.
Lord Turner's key recommendations include:
A change in the role of the FSA - to focus on the strategies of financial firms and wider risks to identify when firms could be heading for trouble
Better monitoring of credit conditions in the UK as a whole to assess if a dangerous boom could be approaching. The FSA, the Bank of England and the International Monetary Fund should do this, Lord Turner says
Banks being required to build up reserves in healthier economic times as a cushion against future losses and being forced to hold more cash or liquid investments, to make them less vulnerable if other sources of finance dry up
The temptation to take excessive risks being removed by making it less profitable for banks to do so - for example, by forcing them to hold more capital
National and international efforts to ensure that remuneration policies - including bonuses - are designed to discourage excessive risk-taking
"Shadow banking" to be overhauled- with regulation for hedge funds and other currently unregulated financial institutions
Credit rating agencies - which judge how stable businesses and investments are - to be regulated
Reforms to the regulation of European banking - including the idea of a new pan-European body to set standards for other regulators to follow.
Failure to look at the big picture was far more important to the origins of the crisis than any specific failures in supervising individual firms
Lord Turner said that too much faith had been put in the dogma that financial markets were always right, and corrected themselves.
New regulation had to look across the financial system internationally, he added, saying "a global market economy remains the best means of delivering global prosperity".
"It requires a global banking system focussed on serving the needs of businesses and households, not in taking risks for quick return. Major changes in regulation and in supervisory approach are required to deliver that," Lord Turner said.
"The approach has to build on a system-wide perspective: Failure to look at the big picture was far more important to the origins of the crisis than any specific failures in supervising individual firms."
International regulation of the banking industry is expected to be one of the key topics discussed at the G20 meeting next month.
BBC business editor Robert Peston said that much of what had been suggested in the report was "common sense".
"Some of its gleaming new rules would in fact represent a return to a framework for limiting risk-taking by banks that prevailed until comparatively recently."
Business Secretary Lord Mandelson agreed that an international regulatory response was required to keep up with the speed of economic change and that this would have given "warnings" of problems in the system.
Robert Talbut, chief investment office of financial firm Royal London Asset Management, said Turner's report was "an inevitable reaction to the events of the last few years".
"I think it also does reflect the fact that the consensus has shifted to wanting banks to be less risky vehicles than they have been in the recent past," he said.
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