FTM is housed in a privately owned building, which is located next to the Kallimarmaro Panathinaiko Stadium.
The Hellenic Post and the Philatelic Associations, in order to collect, preserve and display historical objects, which have been used since the establishment of the Postal Service in Greece, created the FTM. Its foundation was legally established in 1966. In 1977, the building, which houses the Museum to this day, was donated by the philatelist Nia Andreas Stratou and began to operate under the supervision of the Hellenic Post.