The bank's staff are said to have actively concealed where money was going.
The accusations involve transfers to Burma, Cuba and Sudan, as well as Iran and Libya, when the country was still controlled by Colonel Gaddafi.
In a statement the bank said it "acknowledges and deeply regrets [its] failings".
But it pointed out that authorities at the US Justice Department and the District Attorney of New York had both closed related investigations and would not be bringing charges.
Some of the allegations date to 2009, a year after RBS was bailed out with £46 billion of taxpayers' money.
The settlement is the sixth round of fines that the state-owned bank has had to pay this year. Other penalties were imposed following allegations of involvement in rate-rigging.
The latest announcement is another setback for the bank following the surprise departure of finance director Nathan Bostock, who only took up the post on October 1. RBS shares fell yesterday after Mr Bostock's move was met with dismay in the City. RBS's other recent problems include an IT failure last week that left customers unable to use debit or credit cards.
The $100m settlement was announced just hours after Lloyds Banking Group, also part-owned by the taxpayer, was hit with a record fine for another misselling scandal. Lloyds was forced to pay £28m for "serious failings" in a bonus scheme for sales staff.
Last night, Labour MP and Commons Treasury Select Committee member John Mann called on Chancellor George Osborne to "get a grip" on the industry.
Another member of the committee, Tory MP Mark Garnier, called for smaller bonuses at the UK's scandal-hit state-owned banks.
The allegations that RBS broke sanctions were said to involve more than 3500 transactions valued at approximately $523m (£319m).
Bank staff at UK payment processing centres were given a step-by-step written guide to routing US dollar payments to avoid detection, said the New York State Department Of Financial Services.
The instructions read: "Important: For all US dollar payments to a country subject to sanctions, a payment message cannot contain any of the following: 1. The sanctioned country name. 2. Any name designated on the Office Of Foreign Asset Control restricted list, which can encompass a bank name, remitter or beneficiary."
In 2007, our sister paper, the Sunday Herald reported allegations from human rights groups that RBS was "fuelling repression" by propping up the Burmese military regime.
The US Treasury Department said between 2005 to 2009 the bank removed references to sanctioned locations from payment messages to American banks.
RBS launched its own investigation into the issue in 2010. Since then four employees, including its head of global banking services for Asia, the Middle East and Africa and its head of money laundering prevention for corporate markets, have been sacked.
In a statement the bank said it had also committed £300m since 2010 to improve its sanctions controls.
RBS settled with three regulators - the US Federal Reserve, the US Treasury Department and the New York State Department of Financial Services.
Several other UK banks have also settled with regulators over similar claims over Iran, including Lloyds, which in 2009 agreed to pay $350m.
In a statement, the bank said: "RBS plc has co-operated fully with the US Authorities and acknowledges and deeply regrets these failings.
"RBS plc embarked on an extensive remediation plan to address the shortcomings identified in its investigation ... [and] has committed almost £300m [since 2010] to strengthen the bank's control environment on sanctions."