Work and Pensions Secretary James Purnell told MPs the organisation would retain the business, with a new contract running for five years from 2010, with the possibility of an extension beyond that.
The decision was welcomed by subpostmasters and unions, which had warned that 3,000 branches would close if the work was given to a rival bidder.
The contract for the Post Office Card Account was put out to tender, with PayPoint and another firm expressing an interest.
Mr Purnell said that in order to support a viable post office network, the competitive tendering process had been cancelled.
"I firmly believe that this is the right decision for our customers, the Post Office and sub-postmasters. The Post Office is a cherished national institution at the heart of many communities.
"The card account is an important source of income, and brings customers through the doors of post offices across the country.
"Global economic events have made people, particularly the most vulnerable in our society, more concerned about financial transactions. The Post Office is a trusted brand, and is seen as a safe, secure and reliable provider of services in these turbulent times.
"Now is not the time for the Government to do anything to put the network at risk, particularly as post offices are often the only providers of financial services in remote areas."
Around 4.3 million people hold a Post Office Card Account to obtain pensions and benefit payments, including jobseeker's allowance and child benefit.
Around £80m is paid out every day to account holders, with many of them spending some of the money in post offices or shops run by subpostmasters.
The card accounts for one in four visits to post offices, rising to one in two in rural areas and is regarded as a lifeline by workers in the industry.
Alan Cook, managing director of the Post Office, said: "We very much welcome this decision, which enables us to achieve our goal of maintaining a branch network of around 11,500 outlets for the foreseeable future.
"It's great news for Post Office Ltd, for our subpostmasters and for our customers. We will, of course, also be working with other Government departments to drive a wide range of services through the network, while at the same time building on our existing range of financial and other products."
Billy Hayes, general secretary of the Communication Workers Union, said the announcement was "a victory for common sense".
He said: "We're pleased that, following months of extensive campaigning and lobbying by our union, the Federation of SubPostmasters, MPs, customers and all those who care about the Post Office right across the UK, the Government has listened and made the right decision.
"James Purnell has shown good judgment on this matter.
"We hope that today's decision represents a further indication that the Government is now willing to adopt a more positive approach towards the future of this vital public service."
The union has also been urging the Government to use the full potential of the Post Office to create a new Post Office People's Bank.
Liberal Democrat work and pensions spokeswoman Jenny Willott said: "This announcement comes as a huge relief to the millions of Post Office Card Account holders, thousands of sub-postmasters and the countless communities that may have lost their post office if the decision had been different.
"The Government has wasted time and money and caused immeasurable heartache by dragging this process out for so long.
"This could all have been avoided if, as the Liberal Democrats have long argued, the Post Office Card Account had never been put out to tender in the first place.
"However, cancelling the procurement exercise is a peculiar means of arriving at this decision and ministers have some explaining to do."
The Federation of Small Businesses (FSB) also welcomed the decision, saying that some sub-postmasters earned 20 per cent of their income from the Post Office Card Account (POCA).
Spokesman Clive Davenport said: "This is welcome news and underlines the FSB's central campaign to Keep Trade Local. Many convenience stores in towns and villages operate alongside a post office.
"Around £27bn is paid out each year to POCA customers and of that, £2bn is spent in these businesses.
"The Post Office has an unrivalled geographical spread, particularly in rural areas, and awarding the contract to the Post Office will help save thousands of post offices, businesses and jobs."
Shadow business secretary Alan Duncan described the decision as a "humiliating climbdown for the Government, who have done everything they possibly can to find a way of awarding it (the contract) to somebody else".
Mr Purnell told MPs: "I recognise, of course, that this decision will disappoint those other bidders who had reached the final stage of the competition.
"I want to emphasise to the House, as I have done personally to the companies in question, that my decision does not reflect in any way on their ability to have provided the services in question.
"Nor is it a step we have taken lightly. We recognise the importance of competition in the awarding of public contracts.
"But we have concluded that, in these current circumstances, protecting vulnerable groups by preserving a viable post office network justifies the award of a contract outside the competitive process.
"These are exceptional times, and we believe this is a proper and proportionate response."
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