A Â£350 million ($557 million) premium is to be initially paid for the assets, with a further Â£1.3 billion expected to be handed over when the deal is completed.
That is not expected to happen until December 2011, meaning the cost of buying the branches could be adjusted, reports Reuters.
Santander is to add almost two million retail customers, as well as around 250,000 small and medium-sized businesses, to its client base as a result of the acquisition.
RBS, which is still 83 per cent owned by the taxpayer, was told to divest itself of the bank branches as a price for taking billions in bailout funding from the British government.
Stephen Hester, chief executive of RBS, said: "This is an important milestone in our restructuring work and complements the significant momentum behind our recovery plan overall.
"The bank is becoming stronger, which allows an increased focus on serving ongoing customers and improving commercial success; all a pre-requisite for the profitable realisation of taxpayers' stake in RBS."
Mr Hester added that he expects Santander to be a good owner of the assets and noted that the divestment will make the Spanish group a "stronger competitor" in UK banking, especially in the small and medium-sized enterprise sector.
RBS estimated that the transfer of the bank branches to new ownership will take between 12 and 18 months to complete.
Other divestments required from RBS under the EU State Aid rules include its insurance division, Global Merchant Services and its interest in RBS Sempra Commodities - a part of which has already been sold to JP Morgan.
Earlier this week, insider sources told the Financial Times that Santander is also on the brink of agreeing a deal with HSBC to take on $4.3 billion worth of US car loans.
By Tony Aynsley