He is a 1971 graduate of St. Louis Preparatory Seminary North, and received a Bachelor of Philosophy degree at Cardinal Glennon College in Shrewsbury, Missouri, in 1975.
On July 7, 1979, Finn was ordained a priest by Bishop John Nicholas Wurm for the Archdiocese of Saint Louis at All Souls Parish Church.
Finn was named by Pope John Paul II as a chaplain to his holiness in August 2003, upon the recommendation of the Archbishop Justin Rigali.
Finn served as pastor of Our Holy Redeemer Parish in Webster Groves, Missouri, prior to being appointed the coadjutor bishop of Kansas City.
[5] As of December 2011[update], Finn served on the Administrative and the Priorities and Plans Committees for the United States Conference of Catholic Bishops, and had been chairman of the Task Force on the Life and Dignity of the Human Person.
[4] In May 2011, Finn apologized for his failure to act in a more timely manner in the case of Reverend Shawn Ratigan, who was accused of engaging in inappropriate behavior with children.
Finn had received a letter in May 2010 from a Catholic elementary school principal, reporting numerous instances of inappropriate behavior by Ratigan.
Finn's admission came five months after the diocese discovered inappropriate pictures of children on Ratigan's computer, and a week after he was arrested on child pornography charges.
[6][7][8] On June 9, 2011, Finn appointed former U.S. Attorney Todd P. Graves to conduct an independent investigation of diocesan policies and procedures used to address sexual misconduct by church personnel, including Ratigan.
[10] On October 14, 2011, a county grand jury indicted both the diocese and Finn with failing to inform police about child pornography, a criminal misdemeanor.
[16] Cardinal Sean O'Malley from the Archdiocese of Boston criticized Finn's actions in a November 2014 interview with the television news program 60 Minutes.
Finn also welcomed the Institute of Christ the King Sovereign Priest to the diocese to celebrate mass at St. Patrick's Oratory, the oldest church in Kansas City, Missouri.
In a pastoral letter published in the October 24, 2008, issue of the diocesan newspaper, The Catholic Key, Finn referenced the upcoming 2008 US presidential election: "Our Catholic moral principles teach that a candidate’s promise of economic prosperity is insufficient to justify their constant support of abortion laws, including partial-birth abortion, and infanticide for born-alive infants.