The Western General is one of 23 sites around Scotland which will act as vaccination centres for the priority groups.
Scotland’s deputy chief medical officer Nicola Steedman was at the Western General Hospital to see the rollout begin.
She said: “I felt genuinely privileged to see this long hoped for and clinically crucial vaccination programme begin at NHS Lothian’s Western General Hospital in Edinburgh and I would like to sincerely thank all those involved in the vast amount of work which has allowed us to reach this absolute milestone in our Covid-19 response.
“The arrival of these first Covid-19 vaccines is a huge turning point for us all and will protect those most at risk from the serious effects of the virus, but we can’t relax yet.
“Even after the first people are vaccinated it will be important for now that everyone continues to follow the Scottish Government’s guidance for their area and, above all, to follow FACTS.
“These will continue to be the most important things we can do to protect ourselves and others from the virus, as we continue to roll out the vaccination to all of those who need it.”
Welcoming the first Covid-19 vaccinations in Scotland, Health Secretary Jeane Freeman said: “This is obviously a very welcome milestone in our collective fight against the pandemic and I am very grateful to all those who have worked so hard to ensure Scotland is ready to deliver these first Covid-19 vaccinations.
“Science has given us hope and we are starting on a journey which will eventually allow us to return to the lives we want to lead.
“Following clinical advice from the Joint Committee on Vaccination and Immunisation (JCVI) we will begin with those groups which have been prioritised to address 99 per cent of preventable deaths associated with Covid-19.
“These include elderly care home residents and staff, frontline health and social care workers and a number of other groups who are at risk of serious harm and death from this virus.”