The Asset Protection Scheme was set up in 2009 and would have meant that taxpayers had to absorb any losses.
Since then, RBS has been able to get rid of half of the Â£280bn of loans and investments it put into the scheme.
The bank, 82% owned by UK taxpayers, paid Â£2.5bn to use the scheme.
BBC business editor Robert Peston said: “Royal Bank of Scotland has moved a step nearer financial rehabilitation and eventual privatisation.”
However, Treasury Minister Sajid Javid said the government was not planning to sell its stake in the near future.
“We’ve said all along that it’s our intention eventually to return it fully to the private sector and today’s news is a significant step towards that,” Mr Javid told BBC News.