The country's long-awaited tourist season will begin on June 15 with the opening of seasonal hotels, while international flights will be able to fly directly to Greece's main tourist spots from the beginning of July.
A list of countries from which visitors will be able to arrive in Greece will be announced before the end of May.
The selection will be based on “epidemiological criteria” as determined by Greece’s committee of experts dealing with the pandemic.
But the 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.
Mr Theoharis said Greece will be waiting for figures in the UK to improve before Brits are allowed back in.
Balkan and Baltic countries, Germany and regional countries such as Israel and Cyprus are expected to be in the first wave of those whose citizens will be allowed to enter Greece, Mr Theoharis said.
Greece has already begun its first cautious steps to welcoming back domestic tourists as public beaches and major tourist reopened over the weekend.
On Wednesday, health authorities announced one new death and 10 new confirmed coronavirus cases, bringing the total number of dead to 166 and the total number of confirmed cases to 2,850 in the country of nearly 11 million.
But the lockdown has dealt a severe blow to Greece’s economy, which has barely emerged from a brutal decade-long financial crisis that saw a quarter of gross domestic product wiped out. Tourism is a vital part of the economy, and authorities have been anxious to ensure the entire summer season is not lost.
In a televised address to the nation on Wednesday, Prime Minister Kyriakos Mitsotakis said visitors would be subject to sample coronavirus testing and “our general health protocols will be adhered to, without them, however, overshadowing our bright sun or the natural beauties of Greece”.
Mr Mitsotakis noted that Greece has “managed to restrict the spread of the virus”, adding: “We made our country an example to follow in the handling of the health crisis.”
Mr Mitsotakis announced a reduction in consumer taxes on transport from 24% to 13%, which will lead to cheaper boat, plane and bus tickets during the tourist season, as well as a cut on tax on coffee, soft drinks and open-air cinema tickets.
Greece is one of several European countries sounding an optimistic note, as Italy also signalled its intention to welcome back UK travellers.
The news comes a week after health secretary Matt Hancock warned Britons that they were unlikely to be able to go on foreign holidays this summer.
In an interview with ITV's This Morning, Mr Hancock said: “It is unlikely that big, lavish international holidays are going to be possible for this summer.
“I just think that’s a reality of life.”