Kaigama was born in Kona, Taraba, on 31 July 1958. He studied for the priesthood at St. Augustine’s Seminary in Jos. He was ordained a priest on 6 June 1981. At the Pontifical Gregorian University, he earned a doctorate in theology in 1991.
Pope John Paul II appointed him bishop of the newly established Roman Catholic Diocese of Jalingo on 3 February 1994. He was consecrated as bishop on 23 April 1995. The Bishop of Yola, Patrick Francis Sheehan OSA, was the principal consecrator, with co-consecrators Gregory Obinna Ochiagha, Bishop of Orlu, and Athanasius Atule Usuh, Bishop of Makurdi.
On 18 May 2000, Pope John Paul named Kaigama to succeed Gabriel Gonsum Ganaka as Archbishop of Jos.
Kaigama was President of the Nigerian Bishops Conference from 2012 to 2018 and President of the Episcopal Conference of West African Catholic Bishops. He is also chairman of the Plateau State-convened “Interreligious Committee for Peace”. Together with the late Emir of Wase, Alhaji Haruna Abdullahi, he has been involved in promoting mutual understanding between Christians and Muslims.
After the riots in Jos in January 2010, he calmed the situation and clarified the conflict in the international press.
On 25 July 2012, Pope Benedict XVI named Kaigama a member of the Pontifical Council for the Promotion of the New Evangelisation.
In 2014, the Catholic Bishops Conference in Nigeria supported legislation to make participation in a same-sex marriage a crime punishable by 14 years imprisonment. It noted the move as a “courageous act” and a “step in the right direction”. Kaigama argued that the action was “in line with the moral and ethical values of the Nigerian and African cultures”, and blessed President Goodluck Jonathan for not bowing to international pressure: “To protect you and your administration against the conspiracy of the developed world to make our country and continent, the dumping ground for the promotion of immoral practices”.
Kaigama condemned foreign aid programs for a disproportionate emphasis on contraception. In 2014, he said: “In the first place, children die in infant mortality, in inter-tribal wars and diseases, but yet you come to say ‘decrease your population and we will give you economic help.’ We want food, we want education, we want good roads, healthcare. We are being given the wrong things and we are being asked to accept, simply because we are poor.”
Pope Francis named him Archbishop Coadjutor of Abuja on 11 March 2019 and he became Archbishop of Abuja when Pope Francis accepted the resignation of his predecessor, John Onaiyekan, on 9 November 2019.