It found that France had the highest use of e-cigarettes, with the proportion of those who had tried one nearly tripling to 21.3 percent from 7.3 percent.
In the UK the figure rose from 8.9 percent in 2012 to 15.5 percent in 2014 - higher than the European average.
Using data from more than 53,000 people across Europe - with at least 1,000 from each country - the study also found the proportion of people across Europe who consider e-cigarettes dangerous nearly doubled to 51 percent from 27 percent.
E-cigarettes are metal tubes that heat liquids typically laced with nicotine and deliver vapor when inhaled. The liquids come in thousands of flavors, from cotton candy to pizza.
Use of the devices has grown quickly in the last decade, with U.S. sales expected to reach $4.1 billion in 2016, according to Wells Fargo Securities.
Experts fiercely debate whether the devices can help people give up smoking and whether they are safe - with some studies raising concerns about the toxicity of some of the ingredients.
"This research shows e-cigarettes are becoming very popular across Europe - with more than one in ten people in Europe now having tried one," said Filippos Filippidis, who led the European study and published it in the BMJ journal Tobacco Control.
Noting that there are still questions about the long-term risks and benefits of e-cigarettes, he added: "We urgently need more research into the devices so that we can answer these questions."
The average number of people across Europe who had tried an e-cigarette rose by 60 percent between 2012 and 2014, to 11.6 percent from 7.2 percent.
Most people who reported trying e-cigarettes were former or current smokers, although the number who had never smoked tobacco but had tried them also rose.
A Reuters/Ipsos poll on Tuesday found that in the United States use of e-cigarettes and other vaping devices has stalled with about 10 percent of those surveyed using the devices, the same percentage as in a similar poll in 2015.
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