Coccopalmerio was born in San Giuliano Milanese, Italy, where his parents were living during World War II, on 6 March 1938 and raised in Sernio, his mother's home town.

On 10 April 1993, Pope John Paul II appointed Coccopalmerio an auxiliary bishop of Milan with the titular see of Coeliana.

[2] Since 2008, at the direction of Pope Benedict,[3] one of his principal responsibilities has been the revision to procedures for handling clergy sex abuse and the applicable punishments.

[7] On 21 April 2012, Cardinal Coccopalmerio was named a member of the Congregation for the Doctrine of the Faith, the Apostolic Signatura, and the Pontifical Council for Promoting Christian Unity.

[11] The idea was widely appreciated by some cardinals but some were wary that such an appointment would act as a "vice-pope" that would effectively set Vatican and Curial policy[12] or duplicate the already considerable authority of the Substitute in the Secretariate of State, who already fills the role of the Pope's "chief of staff".

[10] On 27 August 2014, Pope Francis named him to a working group tasked with speeding up the process for assessing the nullity of a marriage.

[16][a] Following the first session of the Synod on the Family held in October 2014, he expressed disappointment that not all the participants addressed the pastoral needs of those "who are suffering through problems connected to their relationships" and instead "showed that they simply wanted to reaffirm the doctrine".

[19] In 2017, he said provisions of Amoris Laetitia allow people in irregular marriage access to the sacraments only if they recognize their situation is sinful and desire to change it.

The fact that such a couple also believes changing the situation immediately by splitting would cause more harm and forgoing sexual relations would threaten their current relationship does not rule out the possibility of receiving sacramental absolution and Communion.

[26] An article dated 24 July 2019 on The Jerusalem Post revealed that following his arrest, Capozzi was ordered to undergo drug rehabilitation therapy and was no longer in the Vatican, but rather a spiritual retreat somewhere in Italy.

[27] In the October 2018 issue of the German Catholic journal Herder Korrespondenz, Benjamin Leven, a German theologian and editor of the said journal reported that, according to his own sources, it was Cardinal Coccopalmerio who approached the Pope in favor of the child abuser Don Mauro Inzoli in order to have him partially reinstated as priest.

Leven also alleged that Coccopalmerio is known in Rome for generally opposing the removal of culprit priests from the priesthood, which for him is akin to the "death penalty".

[28] On 16 February 2024, in the premises of the Ambrosianeum cultural foundation in Milan, he participated as a speaker (together with Mario Delpini and Antonio Staglianò) in the conference on the history of relations between the Catholic Church and Freemasonry, organized by the three greater Italian Masonic obediences.