Current drugs to prevent migraine are former epilepsy or heart failure medicines or the anti-wrinkle drug Botox.
However, some patients have migraines that do not respond to any available treatments.
What makes Erenumab different is it is specifically designed for preventing migraine.
It uses antibodies to alter the activity of chemicals in the brain that are involved in both pain and sensitivity to sound and light that comes with migraine.
Trials showed erenumab more than halved the number of migraines each month for around a third of hard-to-treat patients
The Scottish Medicines Consortium approved the drug for use in patients with chronic migraine when other treatments had failed.
But the National Institute of Health and Care Excellence (NICE) - which evaluates drugs for England, but Wales and Northern Ireland tend to follow suit - has rejected the drug.
One in seven people around the world live with the regular agony of migraine
Migraine is up to three times more common in women than men
The Migraine Trust estimates there are more than 190,000 migraine attacks every day in the UK
People with headaches for fewer than 15 days a month have episodic migraine
If it is on more than 15 days it is classed as chronic migraine
NICE's final decision, published on its website, said there was "substantial uncertainty in the evidence for the clinical and cost effectiveness of erenumab".
The price the drug company Novartis is charging the NHS is confidential, but the company insists the cost "reflects the clinical value" erenumab brings to patients.
The British Association for the Study of Headache Council said it was difficult to understand why the treatment was approved in Scotland, but not the rest of the UK.
Its chairman, Dr Mark Weatherall, said: "This drug is not a panacea, but it is an important advance in the scientific treatment of migraine, which effects huge improvements in the lives of many of those who take it.
"It is completely unacceptable that patients in England and Wales who suffer with such a debilitating neurological disorder should be denied access to effective treatment."
Gus Baldwin, the chief executive of The Migraine Trust, said: "This still feels like a very bad day for chronic migraine patients."