Economists say rolling out the scheme would cost up to £991 million but, over the course of a lifetime and across the population, could save as much as £7.2 billion.
The 10% subsidy would do more to change the diets of overweight and obese people than a tax on unhealthy foods, the University of Bath study says.
Healthy foods such as fresh fruit and vegetables, along with some fish and lean meat, should be subsidised.
In practical terms, the scheme would reduce a bag of apples from an average cost of £1.50 to £1.35 and a bag of carrots costing £1 to 90p.
Dr Javier Rivas, from the University of Bath's department of economics, said: "Our results suggest that a subsidy of around 10% on products strikes the best balance between shifting behaviours to encourage healthier eating and saving the taxpayer money in the long run.
"Growing levels of obesity pose a crippling problem for our health service now and in the future.
"Policymakers need to weigh up these new proposals against the long-term costs of overweight and obesity to the health service."
Recent figures suggest that the cost of obesity for the NHS could be as high as £6.1 billion annually, a figure predicted to rise by a further £2 billion by 2030.
Healthy food options cost up to four times as much as unhealthy alternatives, the economists say.
Their research, published in the Bulletin of Economic Research, tested the effectiveness of taxes compared to subsidies and cash incentives at reducing unhealthy food consumption.
Using a detailed mathematical model, they predicted the likely outcomes of each scenario for both the UK and US.
For both countries, their findings suggested that subsidies strike the best balance between effectively changing behaviours and long-term monetary benefits to society.
The study suggests that cash incentives, paying overweight and obese people for making healthier food choices, may be the most effective scheme but the running cost would be too high.
Over the course of their lifetime, each obese person costs the NHS £1,796, the research found. Applied across the population, this accounts for more than 16% of total NHS spend.
A spokesman for the University of Bath added: "This latest study is one of only a few to have examined the effectiveness of different government policies targeting consumers' diets.
"The authors now hope their economic model could be trialled by policymakers."
The study was a collaboration between researchers at the Universities of Bath and Surrey, funded by the institutions.