The main risk factors for the disease are a lack of exercise, smoking, depression and poor education, it says.
Previous research from 2011 put the estimate at one in two cases, but this new study takes into account overlapping risk factors.
Writing in The Lancet Neurology, the Cambridge team analysed population-based data to work out the main seven risk factors for Alzheimer’s disease.
Low educational attainment
They worked out that a third of Alzheimer’s cases could be linked to lifestyle factors that could be modified, such as lack of exercise and smoking.
The researchers then looked at how reducing these factors could affect the number of future Alzheimer’s cases.
They found that by reducing each risk factor by 10%, nearly nine million cases of the disease could be prevented by 2050.
In the UK, a 10% reduction in risk factors would reduce cases by 8.8%, or 200,000, by 2050, they calculated.
Current estimates suggest that more than 106 million people worldwide will be living with Alzheimer’s by 2050 – more than three times the number affected in 2010.
Prof Carol Brayne, from the Institute of Public Health at the University of Cambridge, said: “Although there is no single way to treat dementia, we may be able to take steps to reduce our risk of developing dementia at older ages.
“We know what many of these factors are, and that they are often linked.
“Simply tackling physical inactivity, for example, will reduce levels of obesity, hypertension and diabetes, and prevent some people from developing dementia.
“As well as being healthier in old age in general, it’s a win-win situation.”
Dr Simon Ridley, head of research at charity Alzheimer’s Research UK, said there was still much to discover about the disease.
“While age is the biggest risk factor for most cases of Alzheimer’s, there are a number of lifestyle and general health factors that could increase or decrease a person’s chances of developing the disease.
“However, we still do not fully understand the mechanisms behind how these factors are related to the onset of Alzheimer’s.”
Dr Ridley said there were more than 820,000 people in the UK living with dementia, and an ageing population would lead to spiralling numbers being affected.
“As there is still no certain way to prevent Alzheimer’s, research must continue to build the strongest evidence around health and environmental factors to help individuals reduce their risk.”
He added: “This new study also highlights that many cases are not due to modifiable risk factors which underlines the need to drive investment into new treatment research.”
Of the seven risk factors, the largest proportion of cases of Alzheimer’s in the US, UK and the rest of Europe can be attributed to physical inactivity.