Two people without any underlying health problems have died from the virus - including a 17-year-old pregnant woman from the Borders - although a suppressed immune system can make pregnant women more vulnerable.
In the majority of cases, the vaccine will be administered in a single dose, but children under the age of 10 and in the at-risk group will need two doses.
Health Secretary Nicola Sturgeon told the BBC's Good Morning Scotland programme the vaccine was safe.
She said: "It has gone through extensive safety checks and the European Medicines Agency has given it a licence, so people can have confidence in this vaccine.
"I would simply say to people whatever concerns you have about vaccines, remember swine flu is a virus that, for some people, can lead to very serious complications, and in some cases, to death and that is what makes vaccination so important."
Ms Sturgeon said the first supplies would be available in hospitals for frontline staff and patients with conditions which make them vulnerable to the virus.
"The vaccine will start to be distributed to GP practices from the beginning of next week and it will take perhaps two or three weeks to get it to every GP practice across the country," Ms Sturgeon said.
Dr Harry Burns: ''It seems to me a prudent thing to take this vaccine if you are offered it''
She said people in priority groups would get a letter from their GP in the next few weeks advising them to get the vaccine.
The health secretary added that eligible groups should also be vaccinated against seasonal flu.
Public sector union Unison has also urged its members working in the NHS to take the vaccine.
John Gallacher, secretary to the union's health care group, said: "There should be no shortcuts to safety when it comes to getting the vaccine up and running, and we are glad it has now had its EC license granted.
"Ultimately, having the injection is down to personal choice, but we recommend that members - especially those dealing directly with patients - get the protection."
Bookmark with:
What are these?