The project will test the effects of both types of cigarette on volunteers' blood vessel function, a key health indicator.
It will recruit 135 adult volunteers who have smoked 15 cigarettes a day for a minimum of two years.
The study is funded by the British Heart Foundation.
Participants will be split into three groups, with one continuing to smoke tobacco cigarettes.
The others will switch to electronic cigarettes containing nicotine plus flavour, or switching to electronic cigarettes containing flavour alone.
Dr Jacob George, from the university's school of medicine, said: "E-cigarettes are sold on the principle that they are a much safer alternative to traditional cigarettes because they don't contain harmful substances like tobacco and tar.
"However, many e-cigarettes contain nicotine, which may be harmful to blood vessels itself.
"We want to see whether the e-cigarettes are better for blood vessel function compared to traditional cigarettes.
"Many people seem to think that this is the case but as yet there is no hard scientific evidence to prove this."
People with a history of cardiovascular disease, women who are pregnant or breast feeding and anyone with a nut allergy cannot take part in the study.
Anyone who is interested in joining the study or finding out more should contact vesuvius@dundee.ac.uk
A study comparing the effect of e-cigarettes and tobacco cigarettes on smokers' health is being launched by Dundee University.