There were two accounts of Constantine's 312 conversion story, one by Eusebius and one by Lactantius, and they differ slightly. What they agree on is that shortly before the Battle of the Milvian Bridge on October 28 of that year, Constantine received some kind of divine revelation from the Christian God and proceeded to adopt a Christian symbol as his army's emblem. However, Lactantius states that Constantine saw Jesus in a dream and was told by him to mark his men's shields with the chi-rho sign (the first two letters of Christ in Greek), and that this happened the night before the battle. Eusebius on the other hand claims that he saw a cross in the sky with the words "In this sign conquer" (In Hoc Signo Vinces) during the march through Gaul towards Rome. He is instructed to inscribe this on his battle standard, which he does. The end result is that he defeats his rival for the imperial throne, Maxentius, in battle and takes control of Rome.

There are several issues here. The first is that both Eusebius and Lactantius were personal friends of Constantine, served in his court, and were Christians. Their writings contain clear biases in favour of both Christianity and Constantine throughout so it's hard to know how reliable either of their accounts of the event are. Another is that Constantine, while he showed favour to Christianity throughout his reign (for instance by filling his court with Christians and bestowing them with gifts and legal privileges, not to mention legalizing the practice of it), did not repudiate pagan religious beliefs and practices - he continued to consult the augurs, featured Greek and Roman gods on his coinage, offered libations to the gods at state ceremonies (and serve as Pontifex Maximus, the traditional imperial role as chief priest) and even erected pagan temples and statues in his new capital of Constantinople (to Fortuna and Cybele, among others). The final issue is that all sources agree that Constantine did not submit to baptism (formally convert) until hours before his death. The reason is unknown - perhaps he was trying to wait until all opportunity to sin was over before undergoing the soul-cleansing rite, or perhaps the bishops weren't ready to baptize the ruthless emperor until the end. Either way, it's hard to know today how much of a Christian Constantine was throughout his life and how sincere his conversion was. Did he convert for political reasons? Perhaps, but why go so far to appeal to a religious minority of just 10% of the population? Then again, his references to God were always ambiguous, never specifying the Christian one but using terms like "Supreme God" instead (although his motives for even this can be wondered at). Another thing to consider is that paganism of the time was often henotheistic - someone might prefer to worship one god while acknowledging the existence of others. Constantine may have been like this with the Christian God, a fact that his devoutly monotheistic chroniclers would of course gloss over. At the end of the day, there is just no way of discerning what Constantine's personal and political motives for converting were, or whether he really did convert in 312 or later, or how sincere it all was. Was his deathbed baptism just a formality or did he really wait until then to become a true Christian? We don't know, but hopefully this sheds a little light on the reasons why.

Source: Kirsch, Jonathan. God Against the Gods: A History of the War Between Monotheism and Polytheism. 2004.