Constantine changed Rome by establishing a new capital, which lead to the fall of Rome, and changing the way people reacted to and perceived Christianity. Constantine also contributed to new ideas regarding Jesus and early canon law.
One of the first things Constantine did that changed Rome was create a new capital, Constantinople. This new city helped Constantinople spread a Christian ruling class across the land. However, establishing Constantinople eventually split the Roman empire in two, with an Eastern and Western half. This division lead to the eventual fall of the Roman Empire, with the Western half of the Roman Empire falling approximately 1000 years before the Eastern half.
Constantine also changed the way the public looked at Christianity. His conversion moved Christianity from a religion deserving of persecution to an accepted religion. He not only ended the persecution of Christians, he established Christianity as the official religion of the land.
At the Council of Nicea, Constantine helped settle the matter of Jesus' relationship to God, which settled the issue of Jesus' divinity. Constantine contributed to some changes within the Bible as well as establishing certain religious holidays, such as Easter. He also helped popularize early canon law, which helped him rule.