The initiative for the founding of the Finnish Institute at Athens was taken by the Honorary Consul of Finland in Athens, Konstantinos Lazarakis, and the Chancellor of the University of Helsinki, Nils Oker-Blom. From the beginning, various universities, commercial enterprises and foundations were committed to advance the project of founding the Institute. The aim was to establish a base that would support Finnish researchers and students in their research focusing on Greece. Villa Lante, the Finnish Institute at Rome, founded in 1954, which at that time was the only Finnish Institute abroad, was to serve as a model for the Institute at Athens.

The activities of the Institute started unofficially in the autumn of 1984 when the first Director of the Institute Paavo Castrén arrived in Athens. The Institute was officially recognised by the Greek Ministry of Culture in May 1985 as a result of the cultural contract between Finland and Greece that had come into force. Accordingly, the official inauguration was held on 21 May, the day of Saint Constantine. This particular day, preserved as the anniversary of the Institute ever since, was chosen in order to honour the Consul, Konstantinos Lazarakis, who had supported Finnish researchers and students coming to Greece from as early as the 1950s. The Finnish Institute became the thirteenth foreign and the second Nordic institute in Athens.

At first, the Institute operated in rented premises in Propilaion Street. In 1992 it moved to its own building at 16 Zitrou Street, in the Makriyianni district. The building consists of five offices, a lecture hall and a reference library. In addition, there is a guest apartment, a sauna and a garden. Moreover, since 1987 the Institute lets rooms for students and scholars. Initially, visitors were accommodated in a rented apartment in the neighbouring quarter, and since 1999, in the Koroneos Building, which is named after its donator, Professor Nikolaos G. Koroneos, and which is situated in the Gizi district, to the north of the city centre.