The medicine does not contain the ingredient that produces the high associated with recreational cannabis.
The treatment, called Epidiolex, is based on one of the non-psychoactive components of the cannabis plant, CBD.
Early studies in the US have shown treatment with CBD may reduce the frequency and severity of seizures in children with severe forms of epilepsy.
The new trial marks the first time the treatment has been tested in the UK.
Patients are being enrolled for a trial of the treatment at Edinburgh University's Muir Maxwell Epilepsy Centre, based at the Royal Hospital for Sick Children in Edinburgh, and Great Ormond Street Hospital.
The Royal Hospital for Sick Children in Glasgow and Alder Hey Children's Hospital in Liverpool are also driving the study.
There are further centres in the US, France and Poland.
Their initial focus will be on children with Dravet Syndrome, a rare but serious type of epilepsy that is difficult to treat. Some children will receive the treatment while others will receive a placebo.
In a further phase, researchers will also study the effect on children with Lennox-Gastaut Syndrome.
Only children whose seizures cannot be controlled with existing medications will take part in the trial.
Dravet Syndrome usually takes hold in the first year of life. It causes seizures that are often prolonged, lasting longer than five minutes.
They then develop other seizure types. This has a significant impact on the child's development and can be fatal in some cases.
Epidiolex has been developed by the British biotechnology company GW Pharmaceuticals, which is sponsoring and funding the trial.
Dr Richard Chin, director of the Muir Maxwell Epilepsy Centre, said: "Many children with serious forms of epilepsy do not respond to the medications that we currently have available.
"We need new means of treating these conditions so that we can give back some quality of life to these children and their families."
Children with severe epilepsy could be helped by a new treatment derived from the cannabis plant.