Eames spends his early years in Larne, with the family later moving to Belfast. He is educated at the city’s Belfast Royal Academy and Methodist College Belfast before going on to study at Queen’s University Belfast, graduating LL.B. (Upper Second Class Honours) in 1960 and earning a Ph.D. degree in canon law and history in 1963. During his undergraduate course at Queen’s, one of his philosophy lecturers is his future Roman Catholic counterpart, Cahal Daly.
Turning his back on legal studies for ordination in the Church of Ireland, Eames embarks on a three-year course at the divinity school of Trinity College, Dublin in 1960, but finds the course “intellectually unsatisfying.” In 1963 he is appointed curate assistant at Bangor Parish Church, becoming rector of St. Dorothea’s in Belfast in 1966, the same year he marries Christine Daly.
During his time at St. Dorothea’s, in the Braniel and Tullycarnet area of east Belfast, Eames develops a “coffee bar ministry” among young people but is interrupted by the Troubles. He turns down the opportunity to become dean of Cork and in 1974 is appointed rector of St. Mark’s in Dundela in east Belfast, a church with strong family links to C. S. Lewis.
On May 9, 1975, at the age of 38, Eames is elected bishop of the cross-border Diocese of Derry and Raphoe. Five years later, on May 30, 1980, he is translated to the Diocese of Down and Dromore. He is elected to Down and Dromore on April 23 and that election is confirmed on May 20, 1980. In 1986, he becomes the 14th Archbishop of Armagh and Primate of All Ireland since the Church of Ireland’s break with Rome. It is an appointment that causes some level of astonishment among other church leaders.
Drumcree Church, a rural parish near Portadown, becomes the site of a major political incident in 1996, when the annual Orangemen‘s march is banned by the Chief Constable of the Royal Ulster Constabulary from returning to the centre of Portadown via the nationalist Garvaghy Road after attending worship at Drumcree Church. Public unrest and violence escalates over the next three summers as other parades come under first police and later commission sanction.
Eames, as diocesan bishop and civil leader finds himself immersed in the search for a resolution to the issue. Within the wider Church of Ireland there is unease as it is a broad church in theology and politics including within its congregations nationalists in the south and unionists in the north. Eames, along with the rector of Drumcree, has to navigate this political and social controversy and seeks political assistance to diffuse tension. Some bishops in the Republic of Ireland call for Eames to close the parish church, including Bishop John Neill who later becomes Archbishop of Dublin. He refuses to do so, believing this action could precipitate greater unrest and possible bloodshed.
Eames is, for many years, a significant figure within the general Anglican Communion. In 2003, the self-styled ‘divine optimist’ is appointed Chairman of the Lambeth Commission on Communion, which examines significant challenges to unity in the Anglican Communion. The Commission publishes its report, the Windsor Report, on October 18, 2004.
At the Church of Ireland General Synod in 2006 Eames announces his intention to retire on December 31, 2006. Church law permits him to continue as primate until the age of 75 but he resigns, in good health, at the age of 69. On January 10, 2007, the eleven serving bishops of the Church of Ireland meet at St. Patrick’s Cathedral in Dublin and elect Alan Harper, Bishop of Connor, as Eames’s successor.