Santander, the euro-zone's biggest bank, said the valuation of the deal could be adjusted when it completes, which is expected to happen in December 2011.
The price will be a £350m premium to net asset value, which was about £1.3bn at the end of 2009.
Santander has been in exclusive talks with RBS and has long been the front-runner to buy the branches, attracted by the significant small- and medium-sized business customers.
RBS, 83 per cent owned by the UK taxpayer, was told to sell the branches as a cost of taking billions of pounds in rescue funds from the UK government.
Santander said its parent group had provided £4.46bn of equity capital to its UK business. "The capital will be used to support organic and inorganic growth as well as a planned reorganisation of Group companies in the UK," it said.