Spectators had been banned since last March at the start of the coronavirus outbreak in the country.
The first match with a 10 percent capacity to be allowed will be on Wednesday when Olympiakos hosts French side Marseille for the Champions League group stage contest at the Karaiskaki Stadium in Piraeus, near Athens.
That will be followed by the Europa League group stage match between PAOK Thessaloniki and Omonia of Cyprus on Friday (AEDT).
In addition, one or two Greek Super League games will be allowed to take place with spectators this coming weekend.
The government said that the matches will be a test to see whether the gates should be allowed open for other games in the future.
UEFA has given the green light for matches to be held with spectators under strict health regulations and subject to the approval of that country's governments.
Spectators must wear masks at all times, fans need to stay 1.5 metres apart and remain in their assigned seats.
"Now, finally, the time has come for the gradual return of fans, initially to 10 percent of the capacity of the stands of each stadium and with a maximum number of 3,500 fans. Along with the gradual return of the fans comes the time for responsibility to 100 percent for all of us," the Super League announced.
The league said that the success of the project "will be judged by the attitude of each of us in these unprecedented conditions that the pandemic has imposed on our society".