Known as Erenumab and Aimovig, the drug will now be considered by health officials in England and Scotland to see if it could be made available on the NHS.
Even were it turned down by public health officials, the manufacturer Novartis has said that patients would be able to access the medicine privately from September.
It is designed to block a brain receptor called the peptide receptor, which is believed to be involved in activating migraines - although scientists are not completely sure what causes the agonising headaches just yet.
In drug trials it was shown to reduce the average number of days that patients suffered from a migraine in a month by half.
"Erenumab is the first and only licensed treatment specifically designed to prevent migraine, demonstrating our commitment to developing innovative therapies for people living with some of the most debilitating conditions," said Novartis' UK head Haseeb Ahmad.
Comenting on the news, Wendy Thomas, the chief executive of the Migraine Trust, said: "We think this decision is wonderful as this new treatment has the potential to help many people with chronic and episodic migraine.
"Migraine is incredibly painful, and has symptoms that include vomiting and visual disturbance, so getting it frequently can literally ruin lives.
"That is why it is important that it becomes available to patients as soon as possible."
Source : news.sky.com