The bank will pay $325m to the Commodity Futures Trading Commission, $150m to the US Department of Justice and £875m to the Financial Services Authority.
More than a dozen traders at RBS offices in London, Singapore and Tokyo manipulated the London interbank offered rate (Libor), which is used to price trillions of dollars worth of loans, from at least 2006 until 2010.
The rigging continued even after traders learned that Libor submissions were being probed.
RBS chairman Philip Hampton called it a “sad day” for the bank.
"The RBS board acknowledges that there were serious shortcomings in our systems and controls and also in the integrity of a small group of our employees," he added.
RBS is the third bank to be fined for manipulating Libor, after UBS and Barclays were fined last year.