Ms Sturgeon said that appointments would open to those aged 30 and over today, while over 18s will have the chance to book a booster from later in the week.
However, she warned that the rapid spread of Omicron could mean further restrictions would still be necessary, even with a fast acceleration of the booster campaign.
The news comes as opposition parties urged the Scottish Government to act faster as the race to vaccinate saw long queues and people turned away from booked booster appointments.
There were reports of people waiting outside clinics for hours only to be told to come back another day.
Meanwhile, the World Health Organisation (WHO) said that Scots need to “put in a tough Christmas” to beat Omicron amid warnings from deputy First Minister John Swinney that the virus is “galloping through Scotland”.
The UK’s four chief medical officers recommended yesterday to ministers that the UK go up to Level 4 from Level 3 after a further 1,239 confirmed cases of the Omicron mutation were recorded in the UK as of Sunday. New data revealed that there have been another 38 confirmed cases of the Omicron variant in Scotland in the past 24 hours, taking the total to 159.
Increasing the UK Covid alert level to Level 4 means the epidemic is “in general circulation, transmission is high and direct Covid-19 pressure on healthcare services is widespread and substantial or rising”, according to Government guidance.
In a joint statement, the CMOs said the emergence of Omicron “adds additional and rapidly increasing risk to the public and healthcare services”.
In a press conference last night, Prime Minister Boris Johnson said the UK is "facing an emergency" due to Omicron and said he would also bring England's booster target forward to the end of December.
Mr Johnson said the UK Government is also offering support to the devolved nations to accelerate the pace of the roll out in Scotland, Wales and Northern Ireland too.
Ms Sturgeon said: “I can confirm that urgent work is underway to further accelerate roll out of the booster vaccination programme in Scotland.
“Scotland already has the highest proportion of the over 12 population protected with booster or third doses of all the UK nations. Now, however, urgent efforts are being made to step up the pace even further with the aim of offering a booster jag appointment to all eligible adults by the end of this year if possible.”
She added: “Getting booster jags into people’s arms as quickly as possible is essential given what we now know about Omicron and the importance of boosters in ensuring maximum protection against the new variant.
“Given the expected volume of cases in the weeks ahead, however, it is also possible that further, proportionate protective measures or advice will be necessary. This is true even if Omicron proves to be slightly less severe than Delta.
“The number of cases will still put significant pressure on the NHS and the economy. The government will therefore consider the latest data tomorrow ahead of a Cabinet meeting on Tuesday and I will set out any decisions to parliament later that day.”
There has been increasing evidence that booster vaccinations are key to combating the new variant. On Friday, the United Kingdom’s Health Security Agency said that booster shots give an estimated 70 percent to 75 percent protection against mild disease from the new Omicron variant.
Mr Swinney said yesterday that Scotland was the “most vaccinated” part of the UK and said that 60,000 vaccinations had been administered on Friday alone, but warned that “we should be looking at how we can accelerate the pace”.
However, people turning up to booked appointments for booster vaccinations said they had faced hours of queues, with some turned away and told to come back another day.
Neil Harrison, from Edinburgh, went to his booked appointment for a booster vaccine on Friday afternoon to find huge queues at the Royal Highland Centre at Ingliston.
He said: “I turned up for my appointment on Friday and it was rammed. It is so busy because it’s such a big site and it’s a drop in as well. I have an appointment, but you just all go to the same queue. I queued for over an hour and when I got to the front of one part I spoke to the guy and it looked like it was going to be a while longer, so I had to leave.”
He returned yesterday morning before 8am when the centre opened and got a vaccine quickly, but said that queues were building up behind him as he left.
He said: "I was in and out in less than half an hour today, but my friend was about 15 minutes behind me and he had to wait for an hour. I think it was due to the high number of people using it as a drop in centre, they’ve got so many people turning up.
“To be fair, there must have been 40 people giving vaccinations at a rate of one every three or four minutes, so they are getting through a lot.”
Another man said he had been turned away from a booked appointment at 5pm on Saturday due to a 90 minute wait – then arrived at Ingliston again on Sunday morning to be told that there would be a two hour wait and he should try again another day.
Scottish Conservative shadow health secretary, Dr Sandesh Gulhane said: “It is outrageous that this chaos and confusion is still going on, just when the SNP Government should be doing everything possible to ramp up the booster jag rollout.
“Our vaccination centres can’t even cope with current demand, let alone the huge numbers of younger age groups that will soon be due their booster dose. The SNP Government needs to start moving with the speed and urgency that we saw at the beginning of the vaccine rollout, to ensure we get booster jags in arms, as quickly as possible."
He added: “The SNP must reopen mass vaccination centres – as I have been demanding for weeks – and urgently do more to reach out to the vaccine-hesitant, by taking mobile vaccination centres directly to vulnerable and hard-to-reach communities across Scotland.”
Scottish Labour’s health and covid recovery spokesperson Jackie Baillie said: “The stakes are too high for this kind of chaos. The booster programme is key to keeping us all safe this winter - lives and livelihoods depend on it.
“The SNP must fix these problems and ramp up the programme as quickly as possible.”
A spokesperson for the Edinburgh Health and Social Care Partnership said: “We are seeing high volumes of people walking into our vaccination site at Ingliston for their vaccinations and booster jags which has led to large queues over the last few days.
“It’s great to see so many people take up the opportunity to be vaccinated and we would encourage everyone to use our booking system to help avoid long queues. We would also like to thank the public for their patience as our staff continue to work extremely hard to minimise queuing and vaccinate patients in a safe and timely manner.”
A Scottish Government spokesperson said: “It is welcome news that so many people are taking the opportunity to get vaccinated. Unfortunately, high volumes of people attending drop-in clinics can result in longer waits at peak times.
“The expansion of the online vaccination booking portal to all those over 30, with all those over 18 to be eligible later in the week, will help to alleviate some of this pressure with Health Boards also adding more appointment slots.
“Please continue to take up the offer of a vaccine when you are eligible to protect yourself and others from COVID-19.”
In a TV interview on Sunday, Dr Margaret Harris, spokesperson for WHO, warned that reports from South Africa of a milder form of the virus could not necessarily be applied to Scotland due to the different age demographic in the country.
She said:“Now, the best scenario is that few people end up in hospital because indeed, of the excellent vaccination programme [in the UK] but also, because we'll be taking public health social measures and keeping the transmission down. And that is something that will evolve in the next few weeks. I would love to be talking to you in a couple of weeks after Christmas and saying, ‘Well, we put in a tough Christmas, but look what we achieved’."
The joint statement from the four UK chief medical officers said data on severity of Omicron would become clearer over the coming weeks but hospitalisations from were already occurring and these are likely to increase rapidly.
"The NHS is currently under pressure mainly driven by non-Covid pressures. With a variant spreading with increased transmissibility and reduced vaccine effectiveness, we are likely to see this pressure rise soon."
Mr Swinney yesterday refused to rule out further restrictions in Scotland ahead of a Cabinet meeting on Tuesday, but said that closing down schools and hospitality would be a last resort, while expanding the vaccine passport scheme would also be under consideration.
He said: “Unfortunately, the reality of the situation is that Omicron is quite literally galloping through Scotland. In the space of a week, Omicron has changed from being two per cent of the cases in Scotland, to yesterday, 18 per cent of the cases. So the doubling rate is about just over two days and that compares to other variants of the virus, which were closer to 14 days.
"So that's why I think it's appropriate to use language like ‘galloping through Scotland’ and ‘a tsunami of infections’, because Omicron is coming towards us at a much more aggressive rate and pace than any of the previous variants of the virus. And we have to address that and we have to address it early and swiftly, to protect the population.”