I know I've seen a few great discussions of this before but I'm having a little trouble finding any posts that quite nailed this particular question. As /u/xaethon pointed out, Theodosius became Emperor and brought his Christianity with him, thus beginning a top-down implementation of Christianity as official religion of the empire. However, that's just one part of the story that I'm not qualified or sourced to answer; however, much of /u/xaethon's above linked post are so qualified, so I'll defer to that post.