Travellers arriving from those destinations from 4am on Monday will no longer need to spend 11 nights in a quarantine hotel at a cost of £2,285 for solo travellers.
Just seven countries will remain on the red list following the changes. They are Colombia, Dominican Republic, Ecuador, Haiti, Panama, Peru and Venezuela.
The changes were agreed on a four-nation basis, said the Scottish Government, as UK Government transport secretary Grant Shapps announced the same changes for England.
Vaccine certificates will also be accepted for arrivals from a further 37 countries and territories and those issued under the UN’s vaccine programme.
The Scottish Government did not provide a list of these countries in its announcement, but Mr Shapps said the countries included Brazil, Ghana, Hong Kong, India, Pakistan, South Africa and Turkey.
It means fully-vaccinated people entering Scotland from these locations will be exempt from quarantine and the pre-departure test.
The Scottish Government said details for the UK’s post-arrival testing regime for vaccinated travellers were being finalised, but Scotland would align with it.
No date has been set on when eligible fully-vaccinated arrivals will be able to use a lateral flow test for their day-two test, rather than the more expensive PCR version.
The UK Government has said its “ambition” is for this to be in place “for people returning from half-term breaks by the end of the month”.
Travellers will be able to verify they have completed a lateral flow test by sending a photograph.
Scottish transport minister Graeme Dey said: “It’s important we continue to exercise caution which is why a red list of countries will be retained, carefully monitored and updated following a review at regular intervals.
“If evidence and circumstances change, we will not hesitate to reintroduce restrictions to protect public health in Scotland.
“But the steps we are seeing now pave the way for growth in the travel and tourism sector who we have listened very carefully to and engaged with widely on throughout this difficult period.”