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."

The Scots started their Six Nations campaign with a thrilling first win over Ireland in four years.
They beat France for the first time in 10 years last season at home, but have lost on their past nine trips to Paris.
"It is a long time ago since we won there but we understand there is a reason for that," said Laidlaw.
"France are a good team and it is a hard place to win. We are under no illusions this week - we need to be on top form to get something out of the game.
"We'll need accuracy and we need to be physical and aggressive because the French are big men. But we need to be subtle and clever in our attack.
"If we do that, and move France about and play for 80 minutes, I would back our fitness against them. But we obviously need to be in the game right to the death and not let France get any momentum."
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France have not finished in the top half of the Six Nations since 2011, but impressed in narrow defeats by New Zealand and Australia in the autumn, and came close to a shock victory against England at Twickenham in their Six Nations opener.
"They have improved massively under [coach] Guy Noves and have not been far away from any team they have played," Laidlaw noted. "They have some really dangerous strike runners throughout the team.
"As much as we need to understand why we beat them last year, we need to develop that, be clever and smart and be able to score points.
"We need to keep doing what we are doing well, keep our skills high and if we do that again this weekend, we are going to put ourselves in a strong position.
"The start of the game is massively important, whether it is our kick-off, or or us receiving. It is very important psychologically for them as it is for us.
"If we can start the game playing in the right areas of the field for the first 20 minutes and not muck about too much in our own half, hopefully we will put them under pressure and upset the crowd a little bit."
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Children with severe epilepsy could be helped by a new treatment derived from the cannabis plant.
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Captain Greg Laidlaw says Scotland must be "subtle and clever" as well as match France physically if they are to secure a first win in Paris since 1999.