Which eventually became the official state religion of the Roman Empire?

The Catholic Church was made the sole legitimate creed (and therefore the state religion) by the Edict of Thessalonica issued in 380 by co-emperors Gratian, Theodosius I and Valentinian II.

At that time the Catholic Church was a church which subscribed to the Nicene Creed, a particular interpretation of the trinity and which was opposed to different interpretations by other versions and sects of Christianity. It had two branches, the church of the west (Latin) and the church of the east (Greek). After these two churches split, they came to be called Catholic and Orthodox respectively.

The purpose of the edict was to ban other versions and sects of Christianity which were branded as heretic. It also begun their persecution, particularly that of Arian Christianity, which was popular in the empire. The edict also banned paganism.