The Greek Tourism Ministry said travellers from the permitted countries will be able to enter Greece on direct flights to Athens and to the northern city of Thessaloniki.
The list will be expanded on July 1 to include other countries, the ministry said.
The 29 countries announced on Friday include: Albania, Australia, Austria, North Macedonia, Bulgaria, Germany, Denmark, Switzerland, Estonia, Japan, Israel, China, Croatia, Cyprus, Latvia, Lebanon, New Zealand, Lithuania, Malta, Montenegro, Norway, South Korea, Hungary, Romania, Serbia, Slovakia, Slovenia, Czech Republic and Finland.
The UK was not included.
Visitors arriving from those countries could be subject to sample coronavirus testing, the ministry said.
Greece imposed a lockdown early in its coronavirus outbreak, a move credited with limiting infections.
The country so far has a total of 175 deaths and just over 2,900 confirmed cases.
No cases have been detected on the vast majority of the Greek islands, which are popular vacation spots.
Tourism and related industries make up around 20% of the Greek economy, and the government has been anxious to ensure the tourist season is not lost this year.
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