The Scottish government-commissioned survey found 60% of pupils questioned had seen e-cigarettes for sale in shops, shopping centres or stalls.
About a quarter (26%) had seen outdoor poster adverts.
And 23% of the 2,016 11 to 18-year-olds questioned had seen or heard adverts on TV or radio in the past week.
Although 16% had used an e-cigarette, most had only tried them "once or twice", the survey found.
Only 5% of pupils who had never smoked tobacco had tried e-cigarettes. Curiosity was the main driver for use, sometimes motivated by seeing a friend or family member trying them, the report found.
The forthcoming Health Bill proposes a ban on the sale of e-cigarettes to under-18s, "proxy purchase" by adults for minors and restrictions on the marketing of the products.
Public health minister Maureen Watt said: "This is an extremely useful survey, that gives us one of the first good indications of young people's awareness and experience of e-cigarettes.
"Of particular interest is the large number of children who are being exposed to marketing of these products.
"While more research is needed, e-cigarettes are almost certainly less harmful than tobacco and if people are using them as an aid to quit smoking that is a good thing.
"However, the Scottish Government does not believe that children should have access to them. This is the balance we are aiming for in our forthcoming Health Bill.
"We would consult with stakeholders to consider where exemptions might apply, such as at point of sale where adult smokers who might benefit from e-cigarettes and can find out more about the products."
More than half of secondary school pupils questioned in a study said they had been exposed to e-cigarette marketing.