The alarm was raised at the Tomb Street offices on Thursday morning.
Staff were evacuated as army bomb squad officers carried out tests on a suspicious object.
A number of items have been recovered from the scene.
The PSNI said: "The army examined a suspicious package discovered in the Royal Mail offices. A number of items have been taken away for further examination. Police enquiries are continuing."
Police said the security alert has now ended and the area has been reopened to traffic.