It comes after First Minister Nicola Sturgeon confirmed that the first batches of Moderna had been delivered to Scotland earlier this week.
The jag will be given out at mass vaccination centres in Edinburgh, Glasgow and Aberdeen, as the logistics of cold storage for the vaccine makes it easier to cope with at larger centres.
The Scottish Government said that all health boards will continue to receive a fair share of vaccine.
“The Moderna vaccine, like the Pfizer/BioNTech and Oxford/Astrazeneca vaccines, has gone through a rigorous and independent testing process before being authorised as safe and effective for use,” said Deputy Chief Medical Officer Professor Nicola Steedman.
“I encourage everyone who is offered a vaccine to take up the invitation.
"The vaccination programme is one of three key ways we are working to beat this virus, along with our expanded testing programme to identify cases and break chains of transmission and the important restrictions everyone in Scotland must follow.
"All these measures work to greatest effect to protect people when they work together.”
The UK has bought 17 million doses of the Moderna vaccine, with Scotland set to receive an amount proportional to population – a little under 1.5 million.
Addressing the coronavirus briefing in Edinburgh on Tuesday, First Minister Nicola Sturgeon said: “The fact that we now have three vaccines in use is clearly very welcome and it does give us greater security of supply which is welcome.”
National Clinical Director Jason Leitch said the Moderna doses will not make a particularly large impact on supply in Scotland.
“It will be an additional arm of the vaccine programme but it will not be at the scale we've got yet atround AstraZeneca and Pfizer,” he told a media briefing last week.
"But it will be help, and it will come.”
The Moderna vaccine requires cold storage freezers and specialist equipment, meaning it is more suited to rollout at large vaccination centres with more resources.
Elle Taylor, a 24-year-old unpaid carer, was the first person in the UK to receive a jag, at the West Wales General Hospital in Carmarthen.
Ms Taylor said she hopes the jag will enable her to care for her grandmother “properly and safely”.