Speaking at the coronavirus briefing in Edinburgh on Monday, the First Minister said there is "no current evidence" linking the inoculation to blood clots, after a number of countries, including France, Italy, Germany and the Republic of Ireland suspended its use.
Chief medical officer Dr Gregor Smith also added that findings in the UK showed people given the vaccine in the UK were actually less likely to get a blood clot.
With the vaccination rollout set to ramp up in the coming weeks after supply issues, the First Minister said: "I personally am in the age group that will be vaccinated before mid-April, so I'm hoping to see my blue envelope appear at some point over the next couple of weeks.
"As soon as I get that invitation to go to be vaccinated, I will be there without hesitation, regardless of which of the vaccines I have been offered and I would urge anybody who is getting the invitation to come and be vaccinated to get vaccinated.”
The chief medical officer said the Medicines and Healthcare Products Regulatory Agency (MHRA) monitors notifications from doctors and other healthcare staff who believe adverse effects are caused by new medicines or vaccines.
He said: "What we can say at this point in time, if you look at the data, particularly around blood clots, within Europe and the UK, is that it is no more common to have an episode of blood clot than you would see in the general population.
“In fact, it's somewhat less, if we're being honest, with the number of cases that are being identified here.
"Between one and two in 1,000 people every year would suffer a blood clot and in 17 million or so vaccinations that have been given by this AstraZeneca vaccine so far, we're not seeing any signal coming through whatsoever that suggests there is any more than expected experiencing blood clots within that population."
Prime Minister Boris Johnson has also said that the UK's medicines regulator sees "no reason to discontinue" using the Oxford/AstraZeneca vaccine despite several countries suspending its use.
He said the Covid-19 jab was safe and stressed that the UK's MHRA was one of the "toughest and most experienced" in the world.
Professor Andrew Pollard, head of the Oxford University vaccine group, said while it was right that regulators investigated reports of such side effects, data from millions of people was "very reassuring" that there was no link.
Germany's health minister Jens Spahn said the decision to suspend the vaccine was taken on the advice of the country's vaccine regulator, the Paul Ehrlich Institute, which called for further investigation into seven reported cases of clots in the brains of people who had been vaccinated.
He added that the decision "is a purely precautionary measure".
French President Emmanuel Macron said his country would likewise suspend shots at least until Tuesday afternoon, when the European Union's drug regulatory agency will weigh in on the vaccine.
He said France hopes to resume using the formula soon.