RBS has been trying to reduce its stake in Saudi Arabia's Alawwal Bank as part of efforts to shrink its balance sheet following its state bailout during the 2008 financial crisis.
The 18.6 billion riyal (3.7 billion pound) deal between Alawwal and larger rival Saudi British Bank (SABB) will reduce RBS's stake in the merged group to around 5 percent, compared to a stake of around 15 percent in Alawwal, the source said.
RBS should be able to reduce the capital it holds against the stake, hopefully later this year, the source said, freeing up enough funds to add around 40 basis points to RBS's tier one capital, a measure of a bank's financial strength.
Two other sources close to the merger also said it could be easier for RBS to find a buyer for the smaller stake it will hold after the deal.
The boards of SABB and Alawwal agreed to the takeover on Wednesday in Saudi Arabia's first major banking tie-up for around 20 years.
The source said it also marked a milestone for RBS, bringing the bank's decade-long effort to rid its balance sheet of trillions of dollars in unwanted assets closer to a conclusion.
RBS acquired a stake in Alawwal via its ill-fated takeover of Dutch bank ABN Amro in 2007, which played a big part in RBS's near-collapse and subsequent 45.5 billion pound rescue by the British taxpayer in 2008.
The bank bought ABN Amro as part of a consortium that included Banco Santander and Belgian bank Fortis.
RBS's interest in the consortium was around 38 percent, leaving it with a stake of around 15 percent in Alawwal, the source said.
This amounted to around 5.9 billion pounds in related risk-weighted assets on the bank's balance sheet, which can now be reduced to 1 billion pounds.
RBS remains more than 70 percent owned by the British government.
($1 = 0.7418 pounds)
(Reporting by Emma Rumney. Editing by Silvia Aloisi and Jane Merriman)