RBS, which is 81-per cent owned by the British Government, said it has agreed to pay the equivalent of GBP 391 million to regulators, becoming the third bank to admit its part in the Libor affair after Barclays and UBS.
The investigations uncovered "wrongdoing" by 21 employees, predominantly in relation to the setting of the bank's yen and Swiss franc Libor submissions between October 2006 to November 2010, the bank said.
RBS added it had been fined $325 million by the US Commodity Futures Trading Commission, $150 million by the US Department of Justice (DoJ) and GBP 87.5 million by Britain's Financial Services Authority.
The bank has also entered into a deferred prosecution agreement with the DoJ, in relation to one count of wire fraud relating to Swiss franc Libor and one count for an anti-trust violation relating to yen Libor.
RBS Securities Japan Limited has agreed to enter a plea of guilty to one count of wire-fraud relating to Yen Libor, it added in the statement.
Japan's Financial Services Agency said the Securities and Exchange Surveillance Commission has been investigating the local arm since mid-November for involvement in LIBOR manipulation.
British Finance Minister George Osborne condemned the "totally unacceptable" behaviour at the bailed-out bank and insisted the taxpayer would not pick up the bill.
"Those responsible will face the full force of the law," Osborne told reporters.
The Edinburgh-based lender, which was rescued with taxpayers' cash at the height of the global financial crisis, said that it would recoup about GBP 300 million from its staff bonus pool and by clawing back previous pay awards.
John Hourican, Chief Executive of the bank's Markets and International Banking division, is meanwhile to leave RBS and will forfeit his 2012 bonus and long-term incentive shares.
"This is a sad day for RBS, but also an important one in continuing to put right the mistakes of the past," Royal Bank of Scotland Chairman Philip Hampton said in the statement.
"That is why those responsible have left the organisation or been subject to disciplinary action."
RBS said its derivative traders sought to influence the bank's yen and Swiss franc Libor setters over the four-year period.
"Two RBS traders based in London colluded with other banks and brokers in making and receiving requests for higher and lower" rates, it said.
The total fines slapped on RBS are more than those handed last year to Barclays for attempted Libor rate-rigging, but less than the amount paid by UBS for similar offences.
Libor is a flagship instrument used all over the world, affecting what banks, businesses and individuals pay to borrow money. Euribor is the eurozone equivalent.