Researchers led by a team from the Newcastle University looked at the records of 175,000 children and young people under 21 who had CT (computerised tomography) scans in British hospitals between 1985 and 2002.
They found that radiation exposure received from two to three CT scans of the head in childhood aged under 15, with a cumulative dose of 50 to 60 milligray (a unit of absorbed radiation) can triple the risk of brain cancer later in life.
The same dose to bone marrow would be produced by five to ten head CT scans, which would triple the risk of leukaemia, the researchers found.
While the absolute risk of these cancers occurring after CT is small, radiation doses from CT scans should be kept as low as possible and alternative procedures, that do not use ionising radiation, should be considered if appropriate, the researchers reported in The Lancet.
As radiation-related cancer takes time to develop, the team examined data on cancer cases and mortality up until 2009. It was found that the increased risk of one extra case of leukaemia and one extra brain tumour for 10,000 CT head scans of children aged under ten.
Mark Pearce, an epidemiologist from Newcastle University who led the study, said: "We found significant increases in the risk of leukaemia and brain tumours, following CT in childhood and young adulthood.
"The immediate benefits of CT outweigh the risks in many settings... Doses have come down dramatically over time -- but we need to do more to reduce them. This should be a priority for the clinical community and manufacturers," he concluded.
CT scans, during which an X-ray tube rotates around the patient's body to produce detailed images of internal organs and other parts of the body, are useful for children because anaesthesia and sedation are not required.
CT scans are often prescribed after serious accidents, to look for internal injuries, and for finding out more about possible lung disease. However, potential cancer risks exist due to the ionising radiation used in CT scans, especially in children who are more radiosensitive than adults.
"It's well known that radiation can cause cancer but there is an ongoing scientific debate about whether relatively low doses of radiation like those received from CT scans do increase cancer risks, and if so the magnitude of those risks," added study co-author Dr Berrington de Gonzalez.
"Ours is the first study to provide direct evidence of a link between exposure to radiation from CT in childhood and cancer risk and we were also able to quantify that risk."
In a linked Comment, Dr Andrew J Einstein of New York Presbyterian Hospital said: "This study should reduce the debates about whether risks from CT are real, but the speciality has anyway changed strikingly in the past decade, even while the risk debate continued.
"New CT scanners all now have dose-reductions options, and there is far more awareness among practitioners about the need to justify and optimise CT doses an awareness that will surely be bolstered by Pearce and colleagues' study."