Cottier was born in Carouge, Switzerland, joined the Dominican Order in 1945. Cottier studied theology and philosophy at the Pontificium Athenaeum Internationale Angelicum, the Future Pontifical University of Saint Thomas Aquinas, Angelicum until 1952 obtaining a baccalaurate in philosophy and a licentiate in theology. While at the Angelicum he was ordained a priest in 1951.
He was a professor at the Universities of Geneva and Fribourg. He became secretary of the International Theological Commission in 1989. He was nominated Pro-Theologian of the Pontifical Household in 1990. He was appointed Titular Archbishop of Tullia in 2003 and consecrated on 20 October 2003. He was named Cardinal-Deacon of Santi Domenico e Sisto, the University Church of the Pontifical University of Saint Thomas Aquinas, Angelicum by Pope John Paul II in the Consistory of October 21, 2003. Having served 10 years as a cardinal-deacon, he was promoted to cardinal-priest by Pope Francis on June 12, 2014.
In the run-up to President Barack Obama’s July 10, 2009 meeting with Pope Benedict XVI, Cottier praised Obama’s “humble realism” and compared the president’s approach to abortion to the thinking of St. Thomas Aquinas and early Christian tradition about framing laws in a pluralistic society. Cottier reacted to John Paul II's encyclical Ecclesia de Eucharistia by saying that the Catholic Church rejects the concept of open communion. Cottier defended the Church's view that the embryo is fully a human being. He came out in defense of Pope Pius XII against those who continue to criticize his legacy. Cottier was critical of anonymous Christianity, saying that a theological system that absorbs all realities into Christ ends by turning Christ into a kind of metaphysical postulate of the affirmation of human values, which makes the Church incapable of engaging in serious dialogue, even on the level of human rights. Then, saying that everybody is already of Christ, whether they know it or not, can make the mission futile. Cottier said that the use of condoms may be morally licit in the context of fighting AIDS.
