The Publicis Groupe-owned media agency's Online Video Forecasts report found that the market will expand by a further 19.8 per cent in 2016.
ZenithOptimedia also claims the number of linear TV viewers will begin to decline in 2016 for the first time, after a peak this year. It said the number will rise to 3.1 per cent in 2015, then drop by 1.9 per cent, and then 0.9 per cent in 2017.
The number of people watching videos on mobile devices is expected to grow by 43.9 per cent in 2015, and 34.8 per cent in 2016.
On non-mobile devices the research said that video consumption will rise by 9.5 per cent this year, and by 6.5 per cent in 2016.
In terms of time spent on mobile, ZenithOptimedia said that it is becoming the main platform for viewing online video.
In 2012 the devices accounted for 22.9 per cent of time spent watching online video, globally. In 2014, this increased to 40.1 per cent. ZenithOptimedia expects viewing time to reach 52.7 next year, and 58.1 per cent in 2016.
It means that global online video adspend is also rising "rapidly". The market had an 8.8 per cent share of the total internet adspend in 2012. Last year this rose to 10.2 per cent and it is predicted to increase by 12.8 per cent.
Online video is also the fastest growing sector in internet advertising. The report forecast it to grow by 28.9 per cent to $16.1 billion (£10.3 billion) globally in 2015, 22.5 per cent in 2016 and 19.7 per cent in 2017 to $23.7 billion.
Mark Waugh, the global managing director at Newcast, the branded content arm at ZenithOptimedia, said: "Consumers all around the world are rapidly embracing online video, because it offers them a near limitless array of engrossing content.
"Some of the keenest users are the young, affluent viewers who are hardest to reach on television.
"Brands are finding online video a particularly effective way to reach these valuable audiences, not just with advertising, but also with branded content; content that can inform or entertain consumers in a deeper and richer way than is possible with short, interruptive ads."