The purchase of Swalec - which supplies electricity to homes in south Wales - consists of cash and the repayment of inter-company debt.
British Energy said the move was part of its revised supply strategy, securing in turn higher electricity contract volumes ahead of the new electricity trading arrangements, due to be introduced later this year.
Scottish and Southern has pledged that it will be "business as usual" for Swalec customers.
A spokeswoman for Scottish and Southern said the company could not promise lower bills immediately.
She said there would be a "few" job losses at senior management level, but there would be no compulsory staff redundancies.
British Energy has decided to switch from domestic retail sales to concentrate on wholesale contracting and direct sales to industrial and commercial customers.
Trading alliance
British Energy said it has also agreed with Scottish and Southern a 10-year electricity off-take contract for 10 TWh per annum for the first five years, reducing to 7.5 TWh per annum thereafter.
Scottish and Southern said the transaction will also allow Scottish and Southern Energy to enhance the value of its customer base by offering additional products and services.
The off-take contract is in addition to the existing trading alliance between the two companies, British Energy said.
Scottish and Southern added that the supply prices in the contract would by linked to existing wholesale prices keeping Scottish and Southern neutral to power generation prices.