The home secretary said current laws were “not acceptable to me”, as he announced details of a panel being set up to advise ministers on the changes.
Former Tory leader and foreign secretary Lord William Hague have called for the Class-B drug to be legalised for recreational use, and blasted current laws as “inappropriate, ineffective and utterly out of date”.
Mr Javid ruled out Lord Hague’s proposal, but said he would consider changing the law for cannabis where there was “evidence of medical benefits”.
The review will take place in two parts.
The first will be led by the chief medical officer, and “consider the evidence available for the medicinal and therapeutic benefits of cannabis-based medicines”.
The second will be led by the advisory council on the misuse of drugs, which will report on the potential “harms and public health needs”.
“If the review finds there are significant medical benefits, then we will reschedule (change the drug’s legal status),” Mr Javid promised.
“We have seen in recent months that there is a pressing need to allow those who might benefit from cannabis-based medicines to access them.”
Mr Javid also confirmed a licence has been issued to six-year-old Alfie Dingley.
The child’s mother said she had waited months for Theresa May to fulfil a personal assurance he would be allowed to receive cannabis oil.
Mr Javid said that: “As a father, I know there is nothing worse than seeing your child suffer.
“That is why I have the upmost sympathy for Billy Caldwell, Alfie Dingley and others like them, and for their parents who have been under unimaginable stress and strain.
“I know that they are following a gut parental instinct to do whatever is in their power to try and alleviate their child’s suffering.
“And today I would like to say to this House that I will do everything in my power to make sure that we have a system that works so that these children and these parents get access to the best medical treatment.”
Alfie’s mother, Hannah Deacon, said she was “overwhelmed” by the announcement and that she was now hopeful that it would be easier to access cannabis medication in the future.
She also said she wanted the government to make it easier to research the medical properties of the plant, saying: “Hopefully we will have a more forward thinking way of doing things in this country and medicinal cannabis will hopefully, in five or 10 years time, be the norm.
“That is what I would want, because I would not want any other child to go through what my son has.”
Charlotte Caldwell, whose son Billy was allowed cannabis treatment for his severe epilepsy after the Home Office backed down, said Mr Javid’s comments represented “amazing news”.
Billy’s case sparked widespread calls for a change in the law.
“At every stage of this campaign we have mentioned making history and we have mentioned it because it is common sense,” Ms Caldwell said.
“The power of the mothers and fathers of sick children has bust the political process wide open and it is on the verge of changing thousands of lives by bringing cannabis laws in line with many other countries.
“We are on the threshold of the next chapter of the history book.”
Louise Bostock, from Erdington, Birmingham, has campaigned for years to get cannabis oil treatment made accessible.
Her daughter Jayla has a degenerative brain condition and at one stage was told no other conventional medicine would help her.
Ms Bostock told Sky News: “Cannabis oil has given my six-year-old a life.
“We nearly lost her several times, no mother should ever see what I have seen, it made me determined to do all I can and I have never stopped.
“Today is a good day. A day when they have finally listened. It’s what we have been fighting for for so many years.”
It was revealed back in April that Canada was set to legalise cannabis for recreational use by July next year, making it the first G7 industrialised nation to do so nationwide.
In the US, it is only allowed in the states of Colorado, Washington, Oregon, Alaska, California, Massachusetts, Maine and Nevada.
Other countries, including Australia, Germany and Norway, only allow it to be used for medicinal purposes, while in many parts of the world it is entirely illegal.
In the UK – which is the world’s largest exporter of legal cannabis – those found in possession without a licence face up to five years in prison, an unlimited fine, or both.
Supply and production also result in up to 14 years in prison and an unlimited fine.