The drug uses cannabidiol which unlike THC does not produce a high and will be used to treat rare forms of childhood epilepsy.
Nasdaq-listed GW Pharmaceuticals, which grows its own marijuana plants in glass houses in Britain, hopes the drug will be approved in the UK next year.
The company's chief executive Justin Gover told Ian King Live last week: "This is a new breakthrough in the field of childhood-onset epilepsy. This treatment we have studied for the last five years.
"It has shown in placebo trials it can reduce seizures in certain types of childhood-onset epilepsy and we believe it would a breakthrough in the US and hopefully in the UK next year."
GW Pharmaceuticals is able to extrat cannabidiol, which is just one of about 80 molecules found in cannabis plants. But unlike tetrahydrocannabinol, or THC, it does not produce a high.
The drug, Epidiolex, will be used to treat seizures associated with Lennox-Gastaut syndrome (LGS) or Dravet syndrome in patients two years of age or older.
LGS and Dravet syndrome, which develop in childhood, are rare, severe forms of epilepsy that are notoriously treatment-resistant.
Most patients with LGS and Dravet syndrome require multiple seizure medications and the majority are resistant to currently approved drugs.
The day-to-day impact of these conditions is significant with high rates of early mortality, the company said.
US Food and Drug Administration Commissioner Dr Scott Gottlieb said: "This is an important medical advance. But it's also important to note that this is not an approval of marijuana or all of its components.
"This is the approval of one specific CBD medication for a specific use. And it was based on well-controlled clinical trials evaluating the use of this compound in the treatment of a specific condition."
GW Pharmaceuticals's stock, which has risen almost 50% in the last 12 months on anticipation it would get approval for its drug, fell more than 4% to $144.76 in New York trading.