Who ruled the roman empire the longest?

The longest reigning Roman Emperor was also the first, Augustus. Depending on when you decide his reign began (some people say 31B.C while others say 27B.C) he either ruled 45 or 41 years. There was a 5th Century emperor named Theodosius II who reigned for 42 years, but he ruled over the Eastern Empire only, and acceded to the Imperial thorne at the age of 7. So the answer depends on how you define the reign of Augustus and what exactly constitutes a Roman Emperor. Theodosius II held the power definitively longer than Augustus did, but he never actually ruled from or over Rome, although they Western Empire was still extant at the time.

There was another longer lived emperor from the later Macedonian Dynasty named Basil II. His reign lasted from 10 January 976 to 15 December 1025. This was not the same Roman Empire that Augustus and his early successors had built though. By this time the empire had shrunk to the Balkan Peninsula and Asia Minor. Despite this, Basil ruled over a stable and affluent Empire.

A later emperor of the Palaeologus Dynasty named John V Palaeologus who reigned (on and off between usurpations) from 1341 to 1391. While he held the title Emperor of the Romans, the reality was that the empire had shrunk to the confines of Constantinople and the Despot of Morea in the Greek Peloponess.