In families which own tablet computers, almost a third of children aged under five have their own device, according to a study by the universities of Sheffield and Edinburgh.
Children use their computers for more than an hour a day, researchers say.
The study showed YouTube was the most popular destination.
Jackie Marsh of the University of Sheffield said parents needed to check the appropriateness of what their infant children were using online.
The study revealed the widespread use of tablet computers among toddlers, averaging an hour and 19 minutes on weekdays and slightly longer at weekends.
Most were able to use touchscreens to control the computer and were using them to play games, watch television, films and online videos.
The Economic and Social Research Council-funded project examined computer use in 2,000 families with one or more tablet computers – and found that 31% of under-fives had their own device.
“It may seem surprising that in homes with a tablet, nearly a third of under-fives have their own device,” said Lydia Plowman of the University of Edinburgh.
“But when parents upgrade their tablet, many pass on their older model to their children. Budget models are also popular gifts.”
The study also involved the collaboration of the BBC’s CBeebies service for young children – and CBeebies was found to be one of the most popular apps for this age group.
Other popular online services and games were Disney, Angry Birds, Minecraft and Candy Crush.
Prof Marsh, from the University of Sheffield’s school of education, said that parents needed to watch out for games or apps that are not “age-appropriate” or which do not offer much value for such pre-school children.
She also warned about the adverts and pop-up links that can come with apps and websites.
“The study showed that the use of apps on tablets by pre-schoolers can be very productive and foster a wide range of play and creativity. However, apps need to be chosen carefully by parents for this age group.”
A previous Ofcom study, published earlier this year, had shown that tablet computers were particularly popular with families with children – and among the 5 to 15-year-old age group, 71% of children had access to a tablet device at home.