The significant move was hailed by Chancellor George Osborne as another step towards returning the 80% state-owned lender to the private sector.
RBS will save £1.4 million a day when it exits the Asset Protection Scheme (APS) tomorrow, having paid £2.5 billion since signing up February 2009.
The Chancellor said: "The Government's strategy remains to return RBS to the private sector when it is value for the taxpayer to do so. Today is a step in that direction."
The APS, from which RBS never had to make a claim, provided backstop credit insurance for a portfolio of RBS assets and derivative exposures.
It played an important role in stabilising market perceptions of RBS after the impact of the financial crisis became clearer and the bank's share price fell to a low of 10p in February 2009.
This gave time for the bank's new board and management to put its recovery plan into effect.
The Government agreed to insure £282 billion of assets when RBS formally entered the APS and those assets have since fallen to around £105 billion, a reduction of 63%.
RBS chief executive Stephen Hester, said: "We all want a system in which banks will never again need to seek credit support from Government in a financial crisis.
"Huge progress has been made towards that goal and our exiting the APS is a significant milestone in RBS's recovery.
"The APS has played a valuable role, buying time for the bank as we implemented change from the worrying days of 2009 to create the much stronger institution it is today."
He added: "The changes RBS needed to make after 2008 were truly radical. Much progress has been made along that road. There is much work still under way. But RBS and all who rely on us are better off for the strong progress already made."
Earlier this year, RBS also repaid £163 billion in emergency loans including £36.6 billion in emergency liquidity assistance from the Bank of England, and some £52 billion from the US Federal Reserve, as well as £75 billion from the Credit Guarantee Scheme.
But the bank, along with others across Europe, is still receiving some central bank support via the 10 billion euro (£8 billion) of cheap three-year loans from the European Central Bank's long-term refinancing operation.
The lender faces a number of hurdles ahead, including an expected penalty for Libor-fixing, which is being investigated at RBS after Barclays was fined by regulators earlier this year.
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