The research suggests nine out of 10 people falsely believe nicotine is very harmful to their heath, when in fact it is no more dangerous than the caffeine in a cup of coffee.
Shirley Cramer, chief executive of the RSPH, said: "Getting people on to nicotine rather than using tobacco would make a big difference to the public's health.
"Clearly there are issues in terms of having smokers addicted to nicotine but this would move us on from having a serious and costly public health issue from smoking-related disease to instead address the issue of addiction to a substance which in and of itself is not too dissimilar to caffeine addiction."
The worst damage to health is caused by the tobacco in cigarettes, which - when burning - exposes users to chemicals such as tar and arsenic.
Tobacco also contains some nicotine, but according to the new report, nicotine itself isn't harmful.
Nicotine replacement products, like gum, patches and e-cigarettes, are therefore significantly less harmful than cigarettes themselves, according to the research.
The RSPH is calling for these products to be mandatory in shops that also sell regular cigarettes - offering what they call a safer option to tobacco.
They are also calling for e-cigarettes to be renamed nicotine sticks or vapourisers to distance them from cigarettes.
Yet some medical experts say nicotine itself has some risks.
Dr Hamed Khan, a GP and lecturer at St George's, University of London, said: "Being addicted to nicotine obviously isn't ideal.
"There is some evidence that shows that it may increase the risk of heart disease and also potentially increases your blood pressure."
But he agrees that nicotine replacement products themselves can be a useful tool in helping smokers to quit.