Under the change, anyone who is fully vaccinated or under the age of 18 will no longer need to take pre-departure Covid tests.
They will also no longer be required to self-isolate on arrival until they have received a negative result.
Anyone who tests positive on their lateral flow test will need to isolate and take a free confirmatory PCR test.
The decision by the Scottish Government comes 24 hours after the UK Government confirmed the same changes for travellers entering England from abroad.
Net zero, energy and transport secretary Michael Matheson said: “Given the rapid spread of Omicron last year, it was essential that we took immediate steps to protect public health in Scotland, particularly with regards to international travel.
“We still have significant concerns over Omicron, but we recognise that, now it is the most dominant strain in Scotland and across the UK, it is sensible to review the measures currently in place.
“We also fully understand the impact of the restrictions on staff and businesses in the travel and aviation sectors and these changes demonstrate our commitment not to keep measures in place any longer than necessary.
“However, people still need to be extremely careful when travelling and to remember that both our and other countries' COVID-19 requirements can change at short notice as things can evolve very quickly.
“People should therefore ensure they have travel insurance and carefully check their booking terms and conditions, as well as ensuring compliance with the latest regulations for the country being visited.”