On the death of Archbishop Frederick Cornwallis, he was translated to the see of Canterbury, 26 April 1783, on the joint recommendation of Bishops Robert Lowth and Richard Hurd, both of whom had declined the primacy.
Though not a great ecclesiastic, Moore was an amiable and worthy prelate, a competent administrator, and a promoter of the Sunday-school movement and of missionary enterprise.
He appears to have dispensed his patronage with somewhat more than due regard to the interests of his own family.
Moore married twice, first, Jane Wright (1736 – about 1765), the sister of Sir James Wright, Resident at Venice on 29 April 1763 at Walcot St. Swithin, Somerset, England; secondly, on 23 January 1770, Catherine, daughter of Sir Robert Eden, bart., of West Auckland. He left children; one son, Roger Moore, would go on to be a Canon of Canterbury Cathedral.
Discovery of his coffin
In 2017, during the refurbishment of the Garden Museum, which is housed at the medieval church of St Mary-at-Lambeth, 30 lead coffins were found; one with an archbishop's red and gold mitre on top of it. A metal plate identified one of these as belonging to Moore, with another being that of his wife Catherine.
^The Reverend Mr. John Moore of Christ Church in the University of Oxford and Jane Wright were married on 29 April 1763 at Walcot St. Swithin, Somerset, England. The Revd Mr John Moore of Christ Church in the University of Oxford a Bachelor and Jane Wright of the Parish of Walcot a Spinster were Married in this Chapel by Licence this twenty nineth Day of April in the Year One Thousand and Seven Hundred and sixty threeby me W Davenport Rector of Bredon Worcestershire. This Marriage was solemnised between Us John Moore Jane Wright in the presence of Mary Wright Cathe: Wright
^See John Pearce, Seeking a See, (Standing Committee of the Diocese of Dunedin, 1984), 31