The booster programme is running alongside the local health authority's biggest ever flu vaccination programme.
Most care home residents and staff have already been offered their boosters.
However, the way in which the booster will be delivered has changed from the way the first and second doses of vaccine were administered.
A spokesperson for NHS Borders said: “The way that all vaccinations are delivered in the Borders has changed as part of our primary care improvement plan.
"Vaccinations will now be administered by NHS Borders in community clinics instead of by individual GP practices, however, some vaccinations may still be administered in a practice building by NHS Borders staff.
"Those who are housebound will continue to get their vaccination at home and care home residents will get their vaccination in their care home setting.
"Please do not contact your GP practice to book your appointment as they will not be able to do so.”
Covid-19 booster vaccinations are being offered to the same groups who were prioritised in winter and spring 2020/21, and JCVI Joint Committee on Vaccination and Immunisation) has advised that at least 24 weeks should have passed since receiving the second dose of the Covid-19 vaccine, before a booster is administered.
Also, anyone eligible who has tested positive for Covid-19 must wait 28 days after a positive test to get the Covid-19 booster.
Those aged 80 years and over and adults aged 16 years and over who are on the highest risk list (previously known as the shielding list) will receive their appointment details by post (blue envelope) for their Covid-19 and flu vaccination.
Those aged 70 -79 will receive their letter after that drive, with clinics expected to run from October 30.
People on the highest risk list who were severely immunosuppressed at the time of their last Covid-19 vaccination will be offered a third primary dose instead of a booster.