Boosting levels of education and upping fruit and vegetable consumption would also have a big effect, the British Medical Journal said.
It comes as another study showed dementia patients are missing out on vital early treatments because GPs are being slow to diagnose them.
It is estimated that one million people in the UK will have dementia by 2025. Several risk factors for the disease have been identified, including obesity, high blood pressure and high cholesterol.
But British and French researchers wanted to assess what public health interventions could have the biggest impact on reducing the burden of dementia in the population.
They took a group of 1,400 elderly people and tested them for signs of dementia after two, four and seven years.
Alongside this they recorded height, weight, education level, monthly income, mobility, dietary habits, alcohol consumption, and tobacco use and asked participants to do a reading test as a measure of intelligence.
Eliminating depression and diabetes and increasing fruit and vegetable consumption were estimated to lead to an overall 21% reduction in new cases of dementia. Increasing education would also lead to an estimated 18% reduction in new cases of dementia across the general population over the next seven years, they reported.
By contrast, removing a gene linked with the disease would only cut new cases by 7%.