The umbrella term applied to a person who presides at a marriage ceremony, whether religious or civil, is officiant. From both a religious and legal standpoint, the betrothed couple marries each other and the officiant oversees the ritual and legal niceties of the process.
Wedding officiants oftentimes are ordained members of religious organizations. Judges are also vested with the power to preside at wedding ceremonies. In some jurisdictions, court clerks can serve as wedding officiants. The captains of boats have the power to preside when a vessel is at sea. Laws regarding who officiates at weddings varies from one jurisdiction to another.