Greece will allow travellers from around two dozen countries including Germany, Cyprus and Israel to visit from mid-June without having to be quarantined.
As part of a gradual easing of coronavirus lockdown restrictions, government officials have said that tourists from 20-25 countries will be allowed in.
Tourism accounts for about 20% of the Greek economy and the government sees the sector as a major engine of its recovery from a lockdown that has brought business to a virtual standstill.
"There will be some 20-25 countries whose nationals will be allowed to come," a government source said, adding that the list would include Cyprus, Israel and countries in central Europe and the Balkans.
The full list would be announced this week.
Greece has already said it is likely to ban Brits when it reopens for tourists due to our poor coronavirus record.
Greek tourism minister Haris Theoharis told ITV News that the UK's record on coronavirus is currently not good enough for Britons to be allowed to visit.
“I think that the UK has a big difference in terms of the current medical status of the country with Greece, so I don’t think it’s likely it will be there,” he said.
When figures in the UK improve, Mr Theoharis said Brits would be allowed back in.
Prime Minister Kyriakos Mitsotakis has said Germans will be allowed to visit Greece from June 15.
He has also said that international flights to the northern city of Thessaloniki would resume on June 15, sooner than an initial planned date of July 1.
Greece currently allows citizens from all EU countries except Italy, Spain and the Netherlands to fly into Athens but they are then subject to a 14-day confinement. Visitors from Britain and other non-EU countries are also currently barred from entering Greece.
Italy, Spain and Britain have all seen high rates of infection from COVID-19, the respiratory disease caused by the virus.
Greece has weathered the coronavirus crisis relatively well, with just 2,892 confirmed cases and 173 deaths.
Another government source said health experts were discussing whether travellers would need to have been tested for COVID-19 before visiting Greece and whether insurance coverage for such infections should be recommended.
The government has said it plans to restore international flights to Greece's islands from July 1 but will refuse entry to citizens from countries with high infection rates until July 15.
Some 33 million tourists visited Greece last year, generating revenues of 19 billion euros.
