Alemtuzumab, also known as Lemtrada, can be used to treat NHS patients after it was ruled to be good value for money, despite a £56,000 price tag.
An estimated 9,500 people in Scotland who have the more common relapsing remitting form of MS will become eligible to access the drug following the decision by the Scottish Medicines Consortium (SMC).
Scotland has the highest prevalence of MS in the world, with more than 11,000 people living with the condition.
Originally developed as a cancer treatment, alemtuzumab has been shown to reduce the frequency and severity of relapses, during which patients experience episodes of worsening neurological symptoms over a sustained period. The episodes can last weeks or months, may require hospital treatment and leave lingering health problems.
Trials have shown that the drug also slows down progression of physical disability and offers added convenience to patients, who receive five infusions on consecutive days before returning a year later for three more daily doses, rather than an ongoing regime of injections.
Dr Belinda Weller, a consultant neurologist at the Western General Hospital in Edinburgh, said that while patients would continue to be monitored closely, some would never need another alemtuzumab treatment following the first two courses.
"This is a highly effective drug," she said. "It's up there with the most effective treatments we've got. It might not be for everybody and it comes with potential side effects, but it's another option. Scotland has one of the highest MS prevalence rates in the world, so any new development is important.
"My feeling is that this will be used for those with a very active disease from the outset or who are put on one of the other treatments and still have high relapse patterns."
The drug, which has been developed in Cambridge, was shown to be more effective than interferon injections in trials. It was approved in England earlier this year.
The SMC said that while it was not fully understood how alemtuzumab worked, it rapidly reduced the numbers of two types of white blood cells involved in causing nerve damage in MS patients. MS causes the body's immune system to attack proteins that protect nerve fibres in the brain and spinal cord, disrupting the central nervous system.
Nick Rijke, executive director of policy and research at the MS Society, described the approval of alemtuzumab as a major step forward.
He added: "This drug has taken decades to develop, and while it's not without risk, it's proven to be a highly effective medicine for people with relapsing remitting MS. We look forward to seeing it made available to those who could benefit."
Meanwhile, other treatments approved by the SMC yesterday included injections of rituximab, which is used for non-Hodgkin's lymphoma. The drug had previously been licenced for intravenous use.
However, an application for blood cancer treatment pomalidomide was rejected as it not considered to offer value for money.
Dr Adrian Kilcoyne, medical director for manufacturer Celgene UK, said: "We are obviously disappointed with today's decision, especially since the SMC acknowledged that pomalidomide substantially improved the life expectancy of patients with relapsed and refractory multiple myeloma.
"We will of course do everything we can to try and ensure that patients in Scotland are able to access the treatment and have therefore already re-entered into discussions with the SMC."