From Project Athinai
The Strategeion (house of the strategoi) was erected on the Agora during the Periclean period, somewhere between 449 and 431 BC. The strategoi were the ten generals elected each year to manage military matters. The Strategeion stood on the southwest of the Tholos in an emplacement cut in the slope of the hill. The trapezoidal building consisted of a central courtyard giving access to seven or eight rooms. This poros building measured approximately 20 x 25 m.
On the west side, some 9 m of the bedrock slope of the Kolonos Agoraios (Agora Hill) has been cut out to a depth of up to 2,5 m to make room for the construction of the Strategeion.
Beneath the courtyard, there was a cistern with two water-spouts.
N.B.: another possible identification for this building would be the Poleterion (house of the poletai). The poletai were public administrators working closely with the Boule (assembly).
A Doric propylon was added at the entrance to the forecourt during the 1st century AD.
American School of Classical Studies at Athens; The Athenian Agora: A Guide to the Excavation and Museum, 1990
American School of Classical Studies at Athens; Athenian Agora Excavations - Preliminary Report 2005