So what is set to change and when will it come into effect?
The venues which currently require a vaccine passport for entry will continue to do so for at least another three weeks.
These include nightclubs, unseated indoor events with more than 500 attendees, unseated outdoor events with more than 4,000 people attending, and any event involving more than 10,000 people, seated or standing.
From December 6 however, people will be allowed to show proof of a negative lateral flow Covid-19 test, as well as proof of double vaccination.
More details about the change are set to be published this week, but it is understood that the test will need to be taken within 48 hours of using the certificate, and that NHS text or email notifications received after self-registering a negative test will be accepted as proof.
It is not yet known whether the Covid-19 certification app will be updated, or whether there will be a method of accessing a paper record of a negative test, as is possible with proof of vaccination.
This inclusion of negative testing in the scheme will ensure it remains proportionate, the Scottish Government said, and encourage widespread testing.
Ministers had previously hinted that the scheme may be rolled out to further venues, including cinemas, theatres and other hospitality settings.
However, Nicola Sturgeon announced on Tuesday that this will not be the case.
How does this compare to other countries?
The inclusion of a negative test is in line with the Covid pass schemes already in place in many countries across Europe.
As of last week, there is also a scheme in Wales which allows proof of a negative Covid test within the past 48 hours.
However, almost all of these Covid passes apply more widely than the current scheme in Scotland.
In Wales the pass is used to access cinemas, theatres and concert halls.
In other countries in Europe, a wider vaccine passport has been in use for some time, allowing access to venues including cafes, restaurants, cinemas and gyms.
In Italy and France the pass is also needed for some travel on public transport.