And the more a person smokes, the higher the risk, according to a new report from World Health Organization (WHO) in collaboration with Alzheimer's Disease International.
Even passive smoking could increase the risk, the publication states.
It also highlights that 14 per cent of Alzheimer's disease cases are potentially attributable to smoking, the authors said.
Dr Shekhar Saxena, director of the Department for Mental Health and Substance Abuse at WHO, said: "Since there is currently no cure for dementia, public health interventions need to focus on prevention by changing modifiable risk factors like smoking. This research shows a decrease in smoking now is likely to result in a substantial decrease in the burden of dementia in the years to come."
Serge Gauthier, chairman of Alzheimer's Disease International's medical scientific advisory panel, added: "The research also shows that quitting smoking later in life might be beneficial, so encouraging and supporting current tobacco users to quit should be a priority."
Dr Doug Brown, director of research and development at the Alzheimer's Society, said: "This shocking estimate that so many cases of Alzheimer's may be linked to smoking surely means we must count the global burden of the condition alongside the millions of deaths we already know are caused by tobacco.
"With 44 million people worldwide living with dementia it is now time to rank the condition alongside others like cancer and heart disease when we talk about tackling smoking."