Doctors will be able to prescribe cannabis products to patients from 1 November, Home Secretary Sajid Javid has announced.
The new rule will apply to England, Wales and Scotland, and follows several high-profile court cases.
Mr Javid said the “heartbreaking” accounts of sick children who were fighting to be treated with medicinal cannabis had moved him to take “swift action”.
The plight of young epilepsy sufferers Alfie Dingley and Billy Caldwell came to prominence earlier this year.
Billy was given the NHS’ first prescription for medicinal cannabis oil, a move his mother credited with keeping her son’s seizures at bay.
Alfie’s use of cannabis treatment was said to reduce both the severity and the frequency of his clusters of seizures, coming once every 27 days rather than every 7-10 days.
Hannah Deacon, Alfie’s mother, called it a “momentous day” for families with a suffering child who could be helped by medicinal cannabis.
She said: “We urge the medical world to get behind these reforms so they can help the tens of thousands of people who are in urgent need of help.
“I have personally seen how my son’s life has changed due to the medical cannabis he is now prescribed.
“As a family we were facing his death. Now we are facing his life, full of joy and hope, which is something I wish for each and every person in this country who could benefit from this medicine.”
The decision to legalise medicinal cannabis was made in July, when Mr Javid admitted current laws were “not satisfactory”.
He announced the law change on Thursday, with a promise to monitor the impact of the policy and review it following monitoring by the Advisory Council on the Misuse of Drugs (ACMD).
The recreational use of cannabis will remain illegal.
A Sky Data poll in June found there had been a substantial rise in the number of Britons who thought it should be legalised for medicinal purposes.
Some 82% of those questioned believed it should – an increase of 10% compared with a similar Sky survey in November 2016.
(c) Sky News 2018: Doctors able to prescribe cannabis to patients from next month