The original building was built by Agrippa in the period 27-25 B.C.—the inscription on the exterior still has his name: M. AGRIPPA COS. TER FECIT (Marcus Agrippa, consul for the third time, made [this]). But the dome dates from the reign of the Emperor Hadrian (A.D. 117-138).
The inscription was reproduced on the current building, the original had been destroyed in the fire.