A spokesman confirmed the bank made the discovery in the wake of another foreign exchange rigging scandal in which RBS and four other banks received record fines from the City watchdog.
In 2014, RBS was ordered to pay £217m for its traders’ part in collusion with staff at other banks to manipulate “spot” currency rates, ripping off their clients and distorting the broader market.
The bank said customers would have been unaware they had lost out because they received the rates quoted to them, but that these were not set at the level the bank intended.
RBS made the decision to offer payouts itself, without being ordered to do so by regulators.
The employees responsible, who numbered fewer than 10, had all left the company before their actions were discovered.
The group did not profit from the skimmed cash directly, but would have benefited from bonuses to linked the performance of their department.
Affected customers are being written to and will receive a refund for the extra rate they paid, plus 8pc simple interest, paid automatically into their accounts.
Mike Warburton, a Telegraph columnist and former director at accountancy Grant Thornton, was handed £122 in compensation.