Those who come into contact with a positive case will not need to isolate if they have had two vaccines, and return a negative PCR test.
At least two weeks must have passed since the second dose.
Self-isolation will also be removed for arrivals from Amber list countries from July 19, if they have been double jabbed within a UK vaccine programme.
They must also take a PCR test on the second day after arrival.
In a Covid update to MSPs on Tuesday, Nicola Sturgeon confirmed the country will move to level 0 on July 19.
The move to beyond level 0 on August 9, along with changes to self-isolation from that date, will be confirmed closer to the time.
Self-isolation requirements around school children are still under review, and Ms Sturgeon said an update will be given on this before the start of a new term.
The changes will not affect anyone testing positive, who will still need to self-isolate for ten days.
It comes after the UK Government announced that from August 16, those who have received both vaccine doses in England will no longer need to self-isolate.
This will also apply to anyone under the age of 18, regardless of vaccine status.
Doctors union the BMA has previously called for the relaxation of isolation requirements for healthcare staff in Scotland.
Health boards around the country have warned of high pressure on services caused by staff needing to self-isolate after contact with a positive test.
Scottish Liberal Democrat health spokesperson Alex Cole-Hamilton called for a change to self-isolation requirements for healthcare staff on Tuesday after new figures showed A&E waiting times at their worst level since December.
He said: “A&E departments across the country are dealing with unsustainable pressure.
“We know that the number of people having to self-isolate is spiralling. That’s a real danger to the wider health service and beyond. The staff left behind face a desperate situation, as the workload piles up but there aren’t enough people to cope with it.”
A message from the Editor:
Thank you for reading this article. We're more reliant on your support than ever as the shift in consumer habits brought about by coronavirus impacts our advertisers.
If you haven't already, please consider supporting our trusted, fact-checked journalism by taking out a digital subscription.