Who did contanine move the capital of Rome to Constantinople?

You have already answered you question. Constantine moved the capital to Constantinople, which means City of Constantine. However, he did not move it from Rome. Rome had already ceased to be the capital under the reign of the previous emperor, Diocletian. Diocletian had designated Nicomedia (in northwestern Turkey, just 67 miles east of Constantinople) as the imperial capital of the eastern part of the empire and Milan (in northern Italy) as the imperial capital of the western part.