Javid said on Tuesday that a license to use cannabis-based drugs would also be issued for 6-year-old Alfie Dingley, whose epilepsy causes scores of seizures a day.
He said if a review by the country's chief medical officer identified cannabis-based treatments with "significant medical benefits," they would be legalised.
He said the current legal situation was "not satisfactory for the parents, not satisfactory for the doctors, and not satisfactory for me".
Charlotte Caldwell welcomed the announcement, but said she wanted to hear more details.
"Common sense and the power of mothers and fathers of sick children has bust the political process wide open and is on the verge of changing thousands of lives," she said. "We are on the threshold of the next chapter of the history books."
The cases of Billy Caldwell and other sick children have put Britain's drug laws under scrutiny. On Tuesday, former British Foreign Secretary William Hague joined a growing number of politicians and medical experts calling for the government to legalise marijuana.
The former Conservative Party leader, now a member of the House of Lords, wrote in the Daily Telegraph that the war on cannabis had been lost and that it was "deluded" to pretend otherwise.
He said "cannabis is ubiquitous, and issuing orders to the police to defeat its use is about as up-to-date and relevant as asking the Army to recover the Empire".
The Home Office said in response that "the government has no intention of reviewing the classification of cannabis under the Misuse of Drugs Act 1971 and it will remain a Class B drug" — the middle rung on a three-point scale of illegal drugs.
- AP