The CCC is a prophetic one with a Christian background. The faithful are called Celestians, and the church is sometimes informally called "Cele". The formal name of the church is inspired by a vision by which Jesus would have said that Church members adore him as do the angels in heaven. The name of the church comes from Deuteronomy 26:15: "Look down from thy Holy habitation, from heaven, and bless thy people Israel and the land which thou hast given us, as thou didst swear to our father, a land flowing with milk and honey". The name signifies that they deem themselves as celestial or a representative of the heavenly on Earth. The church claims inspiration from God through the manifestation of the Holy Spirit among the faithful. Its doctrinal teachings are based on the Bible, and any superstition or animist belief from traditional African religions is excluded, as in other churches in the Aladura movement.

The church is governed by twelve major recommendations, consisting of several probitions, including food, common to a number of other monotheistic religions. Tobacco, alcohol and the eating of pork are forbidden. The faithful must not wear their shoes whilst wearing their garments and within the main church. Men and women are separated at the church. Menstruating women and those who have recently given birth are unclean and cannot enter the church building or wear the garment for seven days in the first case after which they would be "sanctified". Members of CCC are forbidden to engage or participate in any form of idolatory, fetish ceremony or cults, black magic and charms. Only men who are "anointed" are allowed access to the altar.

The church uses English language Bibles and the Yoruba translated versions. The church takes elements from Gungbe and Yoruba thought. It also has strong similarities to the "purification movements" against paganism that are relatively common in African Christianity. Oshoffa believed he had a mission to combat "[Satan], 'fetish priests' and other 'powers of darkness'.