Okay I'm on mobile here so bear with me.

First of all, he did not in fact make Christianity the official religion of the Roman empire, that honour goes to emperor Theodosius around 391 with the official banning of pagan practices (almost eighty years after the Edict of Milan, signed by Constantine to make Christianity tolerated).

He was more in favour toleration, he had both Christian and Pagan rites performed at this deathbed. He did however, try to enforce an imperial influence on the Christian church, as demonstrated by his interference in church matters such about an appointment question of bishops office in northern Africa, and his organisation of the Nicaean councils and the council at Tyre.

At the start of his reign only about 10 percent of the Roman world was Christian, at the end, almost 50. Het tried to unify the church by settling disputes and trying to give the emperor control over the ecclesiastical authorities. In building his new capital at Constantinople, he "sought to strengthen and unify the [Christian] community under his command, a community that was to be centered around his new city, which in turn was a microcosm of that world and and reflected his preferr d mix of civic, political and religious life."

As for his miraculous dream and/or miraculous sign of Chi-Rho in the sky, both of these myths (as far as we can say they are myths of course) come from Christian contemporaries or later Christian writers writing decades after the battle at the Milvian bridge (before/during which the miraculous signs are said to have taken place).

Also, about the worshipping of the emperor, this is of course prohibited for Christians - which was the Romans major beef with the religion - Constantine still allowed communities to build tempels to honour and worship him and his families.

Source: Ancient Worlds - A Global History of Antiquity - Michael Scott. Chapters 8 and 9

EDIT: the official change to Christianity is dated to 380, with the "Edict of Thessalonica" or "Cunctos Populus".