The group's CEO said it was "a milestone moment" for the bank
The owner of Ulster Bank has agreed to pay the US Department of Justice US$4.9bn (€4.12bn) as part of a settlement.
This is in relation to the Royal Bank of Scotland's actions in the run up to the global financial crisis.
The department has been examining RBS's issuance and underwriting of US residential mortgage-backed securities (RMBS) between 2005 and 2007.
Under the terms of the proposed settlement, the group has agreed to pay the US$4.9bn (€4.12bn) cash penalty.
Of this amount, US$3.46bn (€2.90bn) will be covered by existing provisions with an incremental charge of US$1.44bn (€1.21bn).
Commenting on the developments, RBS chief executive Ross McEwan said: "Today's announcement is a milestone moment for the bank.
"Reaching this settlement in principle with the US Department of Justice will, when finalised, allow us to deal with this significant remaining legacy issue and is the price we have to pay for the global ambitions pursued by this bank before the crisis.
"Removing the uncertainty over the scale of this settlement means that the investment case for this bank is much clearer."
The proposed settlement is subject to the US Department of Justice and Royal Bank of Scotland entering into a legally-binding agreement.
It clears the way for the British Treasury to sell more shares in the lender, which is currently 71% owned by the UK taxpayer.