RBS was one of the last banks to reach a settlement with the USA government to resolve investigations into its marketing and sale of residential mortgage-backed securities in the run-up to the 2008 financial crisis.
The provisional settlement between the DoJ and RBS follows months of negotiations and takes the total fines banks have paid for the misselling of subprime mortgages in the U.S. to more than £48bn.
The tentative agreement means the government-owned bank would need to take a $1.44bn charge in the second quarter to pay the penalty.
RBS said about $3.6bn of the penalty would be covered by funds already set aside.
Once the world's largest bank by assets, RBS was one of the biggest casualties of the financial crisis which crippled credit, stock and housing markets and upended the global economy.
RBS chief executive Ross McEwan said this was a "milestone moment for the bank".
RBS, however, cautioned that the settlement was subject to the parties entering into a legally-binding agreement, with no assurance that they would "agree on the final terms of any proposed settlement".
Shares in Royal Bank of Scotland Group (LON:RBS) have jumped in London this morning as the bailed-out lender agreed a $4.9-billion preliminary settlement with the US Department of Justice (DoJ) over mis-sold mortgage-backed securities in the run-up to the financial crisis.
The bank a year ago settled a similar case with the U.S. Federal Housing Finance Agency, the conservator of Fannie Mae and Freddie Mac, for $5.5 billion.
The settlement also means RBS can start to pay back the United Kingdom government, who provided the bank with a £45 billion ($61 billion) bailout in 2008.
The settlements have weighed heavily on the bank amid fears over their size.
It moves the bank a step closer to shaking off government ownership.
However, it had said the subprime claims needed to be resolved before it could start selling down its holding.
The incremental charges will be booked in NatWest Markets on a consolidated basis and RBS will retail its guidance on a NatWest Markets consolidated end state (post ring-fencing transfers) common equity tier 1 target of 14pc, as per the outlook statement of its 2017 Annual Report and Accounts.