This will be roughly split between the vaccines developed by Pfizer and by AstraZeneca, and includes “well over” 100,000 first doses already administered.
It comes as the first doses of the Covid-19 vaccine developed by Oxford University and AstraZeneca were given in Scotland on Monday.
The vaccine was approved for use by the Medicines and Healthcare products Regulatory Agency (MHRA) on December 30,
Some 530,000 doses were due to be delivered to the UK this week, with Scotland to receive 8.2 per cent.
Ms Sturgeon said current expectations are that everyone in Scotland over 50 and those under 50 with underlying health conditions, some 2.5 million people, will have been given at least one dose by May.
This is taking into account a recent change in guidance, from an initial plan to give the two doses of the Pfizer vaccine four weeks apart to now delivering them up to 12 weeks apart.
The change in approach from the Joint Committee on Vaccination and Immunisation (JCVI) was supported by medical officers of the four nations.
But the move drew criticism from some who warned the change could confuse or distress vulnerable care home residents and their families.
James Shaw, 82, from Dundee, was one of the first to be given the vaccine, along with his wife Malita, also 82.
He was “delighted” to receive the jab, he said.
My wife and I are delighted to be receiving this vaccination. I have asthma and bronchitis and I have been desperate to have it so I am really pleased to be one of the first to be getting it,” he said.
“I know it takes a little while for the vaccine to work but after today I know that I will feel a bit less worried about going out. I will still be very careful and avoid busy places but knowing I have been vaccinated will really help me.
“All of my friends have said they are going to have the vaccine when it is their turn and I would encourage everyone who is offered this vaccination to take it.”
Associate Director of Public Health Dr Daniel Chandler, Immunisations Co-ordinator, who is overseeing the roll out of the Covid-19 vaccination programme in Tayside said:
“The efforts of our vaccination teams have been amazing and it is testament to a real whole team approach that sees the first over-80s in the general population have their jabs today in Tayside.
“The availability and mobility of the Oxford Astrazeneca vaccine gives us the opportunity to start to roll out the biggest vaccine programme that the UK has ever seen across our communities. Over-80s are the first priority group and patients will be contacted directly to attend a vaccination session.
“Today’s commencement of the community roll-out marks an important next phase in our response to COVID-19. It will act to suppress the virus in our communities to protect those who are most vulnerable, but the plea from all of us in the NHS is keep sticking with all the guidance.”