The available funding would only be for fully electric and plug-in petrol-electric hybrids. As such, currently commercially available hybrids, such as the Toyota Prius, would not be eligible.
There is a limited range of electric vehicles on the market, which range in price from about £8,000 to more than £80,000 for high-performance models.
Sales have been held back by a number of factors: They commonly have a limited range of about 40 miles, take several hours to charge, and have only two seats.
But the government hopes to target drivers of a new generation of all electric or plug-in petrol-electric cars, which are expected to go on sale in two years time.
Business Secretary Lord Mandelson said: "When people see the electric car - the speed, the lack of noise - they are going to fall in love with it."
"We need to lead this green motoring revolution," he added.
Speaking at a racing circuit in Dunfermline, Geoff Hoon said the plan was about "encouraging the idea that electric vehicles will become part of everyday life, that people will take them for granted and they will look and feel the same as any other car".
Jay Nagley, an analyst at Spyder Automotive, said the announcement was very significant for the car industry.
"The big problem is that the next generation of electric cars will initially be very expensive to make - manufacturers say about double the price of a petrol car," he told the BBC.
"Without subsidies, nobody will buy them, so manufacturers won't be able increase production and get the price down."
Mr Nagley added that by 2020 about a quarter of all cars sold could be electric.
But the RAC Foundation, which lobbies on behalf of British motorists, questioned the amount of money being spent by the government, and how it would be put to use.
"If the whole £250m were divided up so £5,000 is allocated per person, this would only put an extra 50,000 electric cars on the road - out of an annual total of some 2.7 million cars sold in the UK," said director Stephen Glaister.
Jorn Madslien, business reporter, BBC News
The future of electric motoring is no longer remote.
Modern lithium-ion batteries have already been installed in prototype cars, such as the Mini E, which handles like an ordinary car and offers a range of 150 miles. But the batteries are huge, so the car has no back seats.
Plug-in petrol-electric hybrids will soon offer five-seat alternatives. In these, a petrol engine takes over once the battery has run out. This is the solution favoured by Toyota.
Alternatively, a small petrol engine recharges the battery whilst driving - the General Motors solution.
Either way, in the future motorists will increasingly buy power from electricity companies rather than from the oil industry.
The Liberal Democrat shadow transport secretary, Norman Baker, said the government scheme was a gimmick that would only benefit the few.
"Discounts on electric cars are all very well for those who can afford to buy a new car but it cannot hide the fact that the government has forced up rail fares and destroyed many local bus services," he said.
Government incentives to stimulate the sales of cars are spreading.
In a separate initiative, Chancellor Alistair Darling is expected to reveal an incentive scheme for motorists to trade old cars in for new ones in next week's Budget.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.