The booster vaccine rollout will also be expanded to everyone over 18, but health secretary Humza Yousaf admitted staffing shortages in the NHS will limit how quickly this can be done.
Boris Johnson has committed to all adults in England receiving a third dose by the end of January, with at least 400 military personnel employed to help and temporary vaccination centres “popping up like Christmas trees".
The Scottish Government has not given a timeline for the delivery of booster vaccines.
In the run-up to Christmas, free lateral flow tests will be widely available in Scotland, including at shopping centres, supermarkets, sports grounds and Christmas markets, Ms Sturgeon said in an update to MSPs on Tuesday.
The tests will come from existing stocks held by the Scottish Government. Following Mr Yousaf’s comments on shortages of vaccine staff, a Scottish Government spokesperson was unable to say whether extra staff will be needed for this testing.
The First Minister urged the public to make use of these tests, to give “the best possible chance” of enjoying a normal Christmas and avoiding further restrictions in coming weeks.
Ms Sturgeon has asked Boris Johnson to agree to UK-wide tougher rules on international travel, which the Prime Minister has so far refused.
A further three cases of the Omicron variant have been identified in Scotland, bringing the total to nine – five in Lanarkshire, and four in Greater Glasgow and Clyde. Across the UK, a total of 22 cases have been found.
None of the cases in Scotland had any link to South Africa or other international travel, Ms Sturgeon revealed on Tuesday, meaning all are the result of community transmission.
They are also all linked to a single private event, held on November 20. None of the infected individuals have been hospitalised and all have been self-isolating since they were tested on or around November 23.
Ms Sturgeon said she expects further cases linked to this event to emerge, and added that it is “almost certain” the variant will spread further in Scotland.
As scientists learn more about the variant, Ms Sturgeon said she hopes levels of concern will reduce rather than increase.
"However, while hoping very much for the best, it is prudent at this stage to contemplate and prepare for something less positive than that,” she said.
"The fact is that any variant which might be more transmissible than Delta – and which could, even to a limited extent, evade vaccine or natural immunity – must be taken seriously.
"That is why we have – and will continue for now – to respond in a way that is proportionate, but also highly precautionary.”
Public Health Scotland is still examining any potential link between the Omicron variant in Scotland and COP26, but Ms Sturgeon said no connection has so far been found.
The First Minister encouraged members of the public to take regular Covid tests and comply with existing protection measures.
“While certainty is not possible until we know more, my hope is that – beyond temporary travel measures – no additional restrictions will be required,” she said.
"However, that will depend partly on what information emerges about Omicron in the days to come, but also and significantly on all of us complying rigorously with all the protections currently in place to stem transmission."
Ms Sturgeon added: “If we treat news of this new variant as an opportunity to raise our guard again, I hope we can protect the progress we have made in recent weeks.
"And we can give ourselves the best possible chance of enjoying not just a more normal Christmas, but a safer Christmas too – and also of avoiding any tighter restrictions in the weeks ahead.”
Amid fears that current vaccines may be less effective against Omicron, Ms Sturgeon outlined an aim to increase vaccine coverage as much as possible, to achieve the maximum protective effect.
The Scottish Government will put new advice from the Joint Committee on Vaccination and Immunisation (JCVI) into practise “as soon as possible”, the First Minister said.
"Urgent modelling work is being done to inform the operational response – for example, assessing the additional capacity that will be needed in terms of workforce and facilities,” she said.
“And as the JCVI has advised, we will continue to prioritise booster jags on an age and risk basis.
“However, the bottom line is that many more people than was the case last week – at least one million more – are now eligible for a booster, and that is good news in our fight against this virus.”
Information will be given to those newly eligible as soon as possible, she said.
Scotland has adequate vaccine supply to deliver these new doses, Mr Yousaf said, but will be limited by a shortage of staff.
“We have adequate supply including with the most recent JCVI advice, but the biggest constraining factor is workforce,” he told the BBC’s Good Morning Scotland on Tuesday.
The Scottish Government had already planned to ramp up the booster and flu vaccine rollout, he said, moving from 500,000 doses a week to 700,000 and involving the need for 440 more whole-time equivalent staff.
With the new JCVI advice, at least a million more people are now eligible for a booster vaccine.
“The NHS is under significant pressure, what we don’t want to do is take people away from really core, important, significant duties ... and get them doing vaccinations,” Mr Yousaf said.
The military has already been called in to help with the vaccination programme in Scotland, with 121 personnel deployed from the beginning of November.
Opposition MSPs urged the Scottish Government to do more to increase vaccination.
“The news of the spread of the new variant will be causing anxiety and concern across the country and so action is needed," said Labour leader Anas Sarwar.
“The Government previously set a target of 400,000 Covid vaccinations a week, but last week only 240,000 boosters were handed out. This must be accelerated.”
The Scottish Conservatives have called for mass vaccination centres to be re-opened.
“There is no doubt that there could be more urgency in delivering the booster jag programme,” said party leader Douglas Ross.
“For several weeks now we have been calling for the reopening of mass vaccination centres to speed up the rollout.
“There is a real lack of urgency from the Scottish Government on this issue, even though we all saw that these centres were incredibly effective in the rollout of the initial doses of the Covid vaccine.”
Ms Sturgeon said mass vaccination centres had high rates of people not attending their appointments, and were inconvenient for some to travel to.