The figure is more than double the amount that Westinghouse's owner, British Nuclear Fuels (BNFL), thought it could get for the Pittsburgh-based business, which is one of the largest nuclear engineering companies in the world.
An announcement that Toshiba has been chosen as the preferred bidder may be made on Thursday, when BNFL holds a board meeting.
That comes hard on the heels of the formal review of Britain's energy policy to be launched today by Malcolm Wicks, the Energy minister.
A team has been set up at the Department of Trade and Industry to look into the possibility of building new nuclear plants in the UK.
The high price of the Westinghouse deal has particularly pleased the Treasury, government sources said.
BNFL is state-owned, so proceeds from the sale will flow directly into government coffers.
Toshiba has triumphed over several other bidders in the auction, including another Japanese company, Mitsubishi, and the American conglomerate General Electric.
Intense bidding between the groups has driven up the price for Westinghouse, which is one of the contenders for the multibillion-dollar programme to build new reactors in China, from about $2bn.
As the three final bidders scrambled to submit their final offers by Saturday's deadline, the price went through $4bn and hit $5bn.
That includes about $600m of historic nuclear clean-up liabilities that the British Government is keen to remove from its books.
Toshiba, whose businesses span electronics, construction and nuclear power, has won the auction despite heightened sensitivity in the US about the decision by the British to auction off Westinghouse, which has been under BNFL's roof since 1999.
As Westinghouse is the developer of some of America's most cutting-edge nuclear technology, a considerable number of US politicians have publicly aired the view that its sale was a national security matter and have said it should go to a US buyer.
It emerged last Friday that President George Bush and the US Commerce Secretary, Carlos Gutierrez, had lobbied Tony Blair and Alan Johnson, the Secretary of State for Trade and Industry, in favour of GE's bid. But the American company did not offer the highest price, making it difficult for Downing Street to lend its support to GE.
There were also concerns that a bid by GE for Westinghouse could be tied up in competition investigations in both the US and Brussels for years because the combined group would control a large segment of the nuclear market.
While Toshiba alone has been awarded preferred bidder status, the company is likely to take on an American partner to try to avoid a clash with some on Capitol Hill who fear that Westinghouse's sale could lead to its technology being passed to potentially unfriendly countries, such as China.
Toshiba is expected to talk to various US nuclear companies, including the Fluor, Louisiana-based Shaw, whose bid for Westinghouse failed at the first round because it was too low, and CH2NHill, a construction management firm, about taking a minority stake in the business.
The high price Westinghouse fetched is seen as vindication by some in Government, and especially the Treasury, who last year pressed for it to be put on the block to take advantage of the renewed interest around the world in nuclear technology as an alternative to fossil fuels.
However, the sale comes as the Government is gearing up to a decision on whether to allow new nuclear reactors in the UK - a scenario which has caused deep concern among anti-nuclear groups and some MPs. Westinghouse and Canada's Candu are favourites to build the plants.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies