Constantine did not create the Church. Individual church groups existed from the earliest days of Christianity, and built a strong, interconnected hierarchy during the second and early third centuries. The first decree legally permitting Christianity to exist in the Empire dates from 311, very shortly before Constantine became at first co-emperor and eventually sole emperor. Constantine was, however, the first emperor to convert to Christianity (at some point in his life); perhaps more importantly, he was the first to patronize financially the Christian Church and God instead of Roman gods. He also made the emperor a power-player in the Church hierarchy.

As far as "merging" paganism with Christianity, it was more like: Constantine worshipped God alone; however, he did so for the same motives previous emperors worshipped the Roman gods. He believed God brought him and his empire prosperity. Constantine conquered Rome in 312 and issued coinage with pagan symbols, built a monument with pagan symbols...then held the entire empire by 325 and built an entire new capital city (Constantinople) to be as free as possible of old polytheistic trappings.

Through various carrot and stick measures, the imperial elite came to convert to Christianity over the next century or so. Measures like only extending the highest government positions to Christians had some success early on; Constantine's successors also gradually banned public sacrifices to the gods, close and destroy temples, and tagged worshippers of the gods with the label paganus: second-class.

The destroyed pagan temples in conjunction with the rich, emperor-funded church building project likely pushed much of the elite to adopt Christianity initially for the same, pagan-ish reasons Constantine did: they believed worshipping God was the key to personal and imperial prosperity. Individual Roman elites might still be pagan, as well as large swaths of rural territory, but the cult of the gods had been divorced from public life.

Certain pagan practices were, well, not exactly absorbed into Christianity, but it is possible to see Christians setting up competing institutions that responded to the same cultural needs. Instead of rural temples to the gods, you see shrines to martyrs and saints. The neutral spirit world of Greco-Roman paganism became the sharply divided angels-demons world of the Christians--further supporting the Christian cult of the saints by allowing many saints to act as exorcists. The Christians promoted their liturgical calendar of feast days to rival pagan holidays. Did workaday peasants at first see the new feasts as parallel to the old ones, except with a new God at the fore? That would just be following the initial pattern of the Roman elite, worshipping God in the same way they had worshipped the gods.

Gradually, though, there was a development of specifically Christian ideas of the sacred. Chris Wickham uses the neat example of caring about burial location in churches even in cities, whereas pagans treated the bodies of the dead as polluted and wanted them as far away from habitation as possible, which has always stuck in my mind.

So, as with most things involving broad-scale changes in thought and belief, paganism faded gradually and "Christianization" happened the same way, despite particular political/legal watersheds like the adoption of Christianity as official imperial cultus and the ban of public sacrifice to the Roman gods.

Good introductory sources: Averil Cameron, Christianity and the Rhetoric of Empire; The Later Roman Empire, 285-430 (which heavily promotes the 'continuity and change' interpretation I detailed above). Peter Brown, The Rise of Western Christendom. Relevant chapters in Chris Wickham, The Inheritance of Rome: Illuminating the Dark Ages.

It wasn't a clean shift, Constantine also tolerated and sometimes even favored the old polytheism. One famous example is that he moved the sabbath from Saturday to Sunday to honor Sol. Sol was one of his favorite gods.

And he built the Arch of Constantine as a dedication to the old gods to honor his victories, and gave sacrifice to the ancient pantheon of gods. This was much after he became a declared Christian. He is juggling the two religions.

So he mostly favored Christianity, and his edicts allowed it to flourish where previously it was suppressed, but the old gods of classical Greece and Rome were certainly not banished. Following Constantine you see the 4th century flip-flopping between official Christianity and polytheism. During this period some emperors, like Constantine, took the stance that the Christian god did exist, but the classic gods also existed. Christianity doesn't become hybridized or changed, but it co-exists with the classic religions.