Tourists from EU countries including Germany, Austria, Denmark and Finland will be able to visit from June 15, the country’s tourism ministry said on Friday.
But some of the world’s worst-affected nations – including the UK, France, Italy and Spain – are not on the list.
More countries could be added before July 1, the ministry added.
Only airports in Athens and Thessaloniki will open on June 15.
Tourists from 16 EU countries will be allowed into Greece including the Czech Republic, Baltic countries, Cyprus and Malta.
Others include Australia, China, Croatia, Israel, Japan, Lebanon, New Zealand and South Korea.
Some visitors could be tested for Covid-19 on arrival, the ministry said.
The list of 29 countries was drawn up “after a study of the epidemiological profile of the countries of origin of tourists and after taking into account announcements of the European Air Safety Agency (EASA), as well as the relevant proposal of the Infectious Disease Committee,” the tourism ministry said.
“Sample testing will be carried out on some visitors from the following countries. The existing rules continue to apply for all other countries.
“The list, which will be expanded starting on July 1, will be announced in time. In any case, the epidemiological monitoring and evaluation will be continuous.”
Tourism minister Harry Theoharis said on Antenna television: “Our aim is to be able to welcome every tourist who has overcome their fear and has the ability to travel to our country.”
Greece, which imposed an early lockdown, has reported 175 deaths and just over 2,900 confirmed cases. Most of the country’s islands have no reported cases.
The UK Foreign Office continues to advise against all but essential foreign travel while the government is set to impose a 14-day quarantine on arrivals from June 8 – a measure facing growing opposition from the travel industry and MPs.