Koch was born on 13 June 1954 in Düsseldorf, Germany He studied theology, philosophy and education at the University of Bonn and completed his examinations in education science. He was ordained a priest of the Diocese of Cologne on 13 June 1980, his 26th birthday. He held a variety of positions in Cologne and was often involved in youth ministry. While doing parish work he earned a doctorate in theology with a dissertation on the significance of liberation in Christian religious education. Since 1995 he has been president of the Federation of Historic German Shooting Clubs. Beginning in 2002 he served as Pro-Vicar General and Secretary General for the committee that organized the celebration of World Youth Day in Cologne in 2005. On 17 March 2006, Pope Benedict XVI named him auxiliary bishop of Cologne with the titular see of Ros Cré. He was consecrated a bishop on 7 May 2006 by Joachim Meisner, Archbishop of Cologne, with Manfred Melzer and Rainer Maria Woelki as co-consecrators. He chose as his episcopal motto the Latin phrase Gaudete semper Dominus prope, "Rejoice always, the Lord is near", taken from the Epistle to the Philippians. On 18 January 2013, Benedict XVI named him Bishop of Dresden-Meissen, and he was installed there on 16 March. In December 2014, he warned against dismissing the concerns of anti-immigrant demonstrators. He said: "While we remain committed to the basic right of asylum for refugees from war areas and victims of political persecution, we must ask ourselves what drives such a large number of people on to the streets every Monday and not tar them all with the same brush by a priori labeling them right-wingers."
On 8 June 2015, Pope Francis named Koch Archbishop of Berlin. Following the procedures revived in 1989 following the reunion of Germany, Koch was first elected by the Berlin church and Pope Francis, seeing no objection, made the appointment. Koch was installed in Berlin on 16 March. The German Bishops' Conference selected him in 2014 to chair its Commission for Marriage and the Family. The German Bishops' Conference selected him as a delegate to the Synod on the Family, which met in Rome in October 2015. In February 2015, discussing the issues facing the synod, he said the church needed a new approach to pastoral care of homosexuals, "a different language", and that to "portray homosexuality as a sin is hurtful". He added: "I know gay couples who value reliability and commitment and live these in an exemplary manner." As the Synod approached, he expressed concern that its focus was shifting from the pastoral concerns it was meant to address to "mega issues such as the understanding of the Eucharist, the issue of church authority and its limits and the question of the definition of marriage". He said "It would have been better to limit the number of topics up for discussion" and "We must not give the impression that the synod spent most of its time quarreling about the conditions for admission to the sacraments." At the synod, the German language discussion group elected him their relator. He told the Synod that theological arguments against allowing Catholics in irregular marriages to receive Communion "do not silence the questions in the hearts of people". He said: In February 2016, joining an alliance with the German Evangelical Church called the Alliance for Cosmopolitanism Koch spoke on behalf of the German Bishops Conference: "Those who contribute words or deeds to the exclusion and reduction of refugees and migrants can not base that on Christianity. Human hostility and stranger hatred are not only in clear contradiction to the values of our free-democratic constitution, but ultimately bear witness to a deep disregard for the Christian message." He has at other times called for special attention to the needs of Christian refugees, who are sometimes mistreated as a minority among the refugee population, and for refugees who are homosexual or transgender. Koch, though an advocate for reconciliation between the Church and the LGBT community, denounced the German Bundestag's vote to legalize same-sex marriage on 30 June 2017. He said "As a Church, we respect same-sex partnerships in which mutual responsibility and care are taken" but he argued for maintaining a distinction between same-sex and different-sex relationships: "differentiation isn't discrimination, and same-sex cohabitation can be valued through other institutional arrangements without opening up the legal institute of marriage".