A tax on the drinks - which the experts argue are linked to "ill health" and have "no beneficial nutrients" - could cut the number who are obese by 180,000 alone.
If the tax was introduced now, they would expect to see these reductions over the next 10 years.
People aged 16 to 30 - who consume the most sugary drinks - would see the biggest effects.
Experts from Oxford and Reading universities worked out that a 20% tax would put about 12p on a 330ml can of fizzy drink bought in a supermarket.
A typical sugary drink contains between six and 15 teaspoons of sugar, with one teaspoon containing 16 calories.
Modelling by the team this month showed a 500ml bottle of Coca-Cola, which contains 210 calories and 14 teaspoons of sugar, would see its price jump from £1.15 to £1.38.
A two-litre bottle, which has 55 teaspoons of sugar, would go from £1.98 to £2.38, while 500ml of Ribena, which has 13 teaspoons of sugar, would jump from £1.18 to £1.42.
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Writing in the British Medical Journal (BMJ), the experts said: "Good evidence shows that regular consumption of sugar sweetened drinks is associated with ill health - principally, adverse weight gain, type 2 diabetes, cardiovascular disease and dental caries.
"As sugar sweetened drinks are weak appetite suppressants, a reduction in their consumption is likely to lead to a reduction in calorie intake, with people being unlikely to seek alternative sources of calories.
"Sugar sweetened drinks are non-necessities and contain no beneficial nutrients, so direct harm from reducing consumption will not occur."
The researchers said the tax "is predicted to reduce the number of people in the UK who are obese by 1.3% or 180,000 people, and the number who are overweight or obese by 0.9% or 285,000 people".
There would be around a 15% drop in the number of sugary drinks bought, with people mainly switching to diet drinks and tea and coffee, they added.
The expected reduction in calorie intake would be 28 calories per person per week.
At present, on average, people aged 16 to 29 drink around 300ml of sugary drinks per day, compared to just 60ml among those aged over 50.
The study said the tax would be expected to raise over £275 million each year (around 8p per person per week).
This saving "could be used to increase NHS funding during a period of budget restrictions or to subsidise foods with health benefits, such as fruit and vegetables".
The research used data on the prices and purchasing of drinks and foods from the Living Costs and Food Survey 2010.
This is a sample of food and drink purchasing among more than 12,000 people and uses two-week food expenditure diaries.
Dr Adam Briggs, of the British Heart Foundation (BHF) health promotion research group at Oxford University and joint first author of the study, said: "Sugar sweetened drinks are known to be bad for health and our research indicates that a 20% tax could result in a meaningful reduction in the number of obese adults in the UK.
"Such a tax is not going to solve obesity by itself, but we have shown it could be an effective public health measure and should be considered alongside other measures to tackle obesity in the UK."
Dr Oliver Mytton, of Oxford University and the other joint first author, said: "Younger adults and children consume much greater quantities of sugary drinks.
"This is a concern for their health, not only in terms of diabetes and obesity, but also tooth decay.
"Our work suggests that a sugary drinks tax would have a much greater impact in terms of reducing obesity in younger adults."
Simon Gillespie, chief executive of the BHF, which helped fund the study, said: "Guzzling fizzy drinks is now the daily norm for around 40% of 13-year-olds.
"The effects on young people's health are a major concern. We know that drinks loaded with sugar can affect our weight, increasing the risk of type 2 diabetes and coronary heart disease.
"This research suggests that a health-related food duty, alongside other measures such as the new front of pack food labelling scheme, could be an effective way - particularly in young people - to help reduce obesity."
Professor Richard Tiffin, from the University of Reading, said: "Obesity is a ticking time bomb. Doing nothing risks condemning millions of people to poor health and an early grave.
"This is a complex battle in which a soft drinks tax could be a useful weapon, but on its own would not go far enough in the face of such a massive problem.
"Sedentary lifestyles, poor education, addiction to alcohol and tobacco, and poverty all play far more significant roles than fizzy drinks in causing bad health.
"Taxing food is a big step, especially when spiralling bills are already making households poorer, and will make very little difference if people are unable or unwilling to make healthier choices elsewhere in their lives."