In contrast, the Conservatives said they would get rid of the tripartite system.
"We will put the Bank of England in charge of the prudential supervision of banks, building societies and other significant financial institutions," Mr Osborne said.
The party would create a separate consumer and markets regulator, effectively spelling the end of the FSA, the BBC's business editor Robert Peston said.
In a statement to the House of Commons, Alistair Darling said the financial system needed to ensure robust regulation, and banks and financial institutions should be better managed.
Some of the key proposals included:
• More help for consumers - a national money advice line funded by the banks and a strengthened deposit protection scheme
• Greater competition - the FSA and Office of Fair Trading to ensure that new players can enter the banking market
• Executive pay - the FSA to report yearly on whether banks have met the new code of conduct on remuneration, and bank boards to be strengthened
• Tougher banking regulation - banks required to hold more capital to cover any future losses and more powers for regulators to take over failing banks
• A new Council for Financial Stability - the FSA, the Bank of England and the Treasury to meet regularly and report on the systemic risks to financial stability.
"What I want to do is make sure that in future when the Bank of England or the FSA or anyone else starts flagging up threats to the economy there is a formal statutory body that has to consider these warnings and then do something about it," Mr Darling told the BBC.
In the House of Commons, he also said that financial institutions needed to be better managed.
"We need a change of culture in the banks and their boardrooms, with pay practices that are focused on long-term stability, and not on short-term profit.
"The FSA now has powers to penalise banks if their pay policies create unnecessary risks and are not focused on the long-term strength of their institutions."
The BBC's business editor Robert Peston said the chancellor was attempting to strengthen the current regulation system.
In practice, the Bank of England, the FSA and the Treasury are supposed to work closely together and share information between themselves, while taking a lead in their own specialised areas.
But the system has been criticised by parliamentary committees for the institutions failing to communicate adequately with each other, and for not making it clear who would be in charge in a crisis.
Shadow chancellor George Osborne criticised the lack of clear lines of responsibility in financial regulation. He said instead of "clarity", Mr Darling's proposed new system would bring "confusion".
There will be champagne corks popping all over the City this afternoon - the chancellor's statement proves that it really is business as usual
Vince Cable, Lib Dem Treasury spokesman
Liberal Democrat Treasury spokesman Vince Cable also expressed disappointment at the reforms.
"This is not so much a White Paper as a blank paper.
"Mr Darling should have used this opportunity to assert his authority over the banks - instead he is maintaining his passive role in [the government's shareholding body] UKFI, which is just not good enough.
"There will be champagne corks popping all over the City this afternoon. The chancellor's statement proves that it really is business as usual."
The British Bankers' Association (BBA) said banks recognised the need for change and would continue to work with authorities to ensure the "long-term success of the UK economy and the banking sector".
"We believe appropriate and effective regulation, capital applied according to risk and good quality supervision are the cornerstones of a vibrant banking community, " said BBA chief executive Angela Knight.
"We welcome moves to create better coordinated financial stability jointly with the FSA and the Bank of England."
The consumers association Which? welcomed measures to increase protection for bank customers.
"We're pleased that the government recognises the need to provide a better deal for consumers," said Which? chief executive Peter Vicary-Smith.
"Warnings about risky products, universally available money guidance and more choice on the High Street will all help to empower consumers in their dealings with the financial world."
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