Vann was ordained to the priesthood by Bishop Joseph McNicholas on May 30, 1981. He then furthered his studies in canon law at the Pontifical University of St. Thomas Aquinas in Rome, residing at the Pontifical North American College. It was at the Angelicum that in May 1985 that he earned his Doctor of Canon Law degree. Upon his return to the United States in 1985, Vann served as parochial vicar at Blessed Sacrament Parish in Springfield until 1990. He served as judge, defender of the bond, and on the diocesan tribunal from 1985 to 1994, also serving on the metropolitan court of appeals for the Province of Chicago. Between 1989 1990, he was also parochial administrator of St. Mary Parish in Pittsfield, Holy Redeemer Parish in Barry, and Holy Family Parish in Griggsville. Vann was pastor of St. Benedict Parish in Auburn and later of Our Lady of Lourdes Parish in Decatur. While serving at Our Lady of Lourdes, he was concurrently a judicial vicar for the Interdiocesan Tribunal of Second Instance for the Province of Chicago and parochial administrator of St. Isidore Parish in Bethany, Sacred Heart Parish in Dalton City, and Our Lady of the Holy Spirit Parish in Mount Zion. He was also dean of the Decatur deanery from 1996 to 2001, and became the bishop's contact for the Hispanic ministry in 1999. He also taught canon law at his alma mater of Kenrick-Glennon Seminary in St. Louis. Vann became pastor of Blessed Sacrament Parish in 2001. In addition to his pastoral duties, he was also named vicar for clergy in the diocesan chancery. He was raised to the rank of Honorary Chaplain to His Holiness on February 19, 2002. During his tenure at Blessed Sacrament, he oversaw a $2.2 million capital campaign for refurbishing the church, as part of the celebration of the 75th anniversary of its completion in 1930. In April 2004, Vann said that he would be "reticent" in giving communion to Senator Dick Durbin, a former parishioner at Blessed Sacrament whose "pro-choice position puts him really outside of communion or unity with the Church's teachings on life."
On May 17, 2005, Vann was appointed coadjutor bishop of Fort Worth, Texas, by Pope Benedict XVI. This was to have been his first assignment as a bishop, but the bishop of the diocese, Joseph Patrick Delaney, died on July 12, 2005. Vann received his episcopal consecration, as previously planned, the next day, July 13, from Archbishop José Gómez, with Archbishop Raymond Burke and Bishop George Lucas serving as co-consecrators, at the Daniel-Meyer Coliseum. He selected as his episcopal mottoIn Fide Et Dileccione In Christo Iesu, In the faith and love in Christ Jesus. During the 2008 presidential election, Vann and Bishop Kevin Farrell issued a joint statement in which they declared that "We cannot make more clear the seriousness of the overriding issue of abortion—while not the only issue—it is the defining moral issue, not only today, but of the last 35 years... As Catholics we are morally obligated to pray, to act, and to vote to abolish the evil of abortion in America." Within the United States Conference of Catholic Bishops, Vann is a member of the committees on marriage, family life, laity and youth, and the subcommittee on marriage and family life.
Bishop of Orange
On September 21, 2012, Pope Benedict XVI announced the transfer of Vann from Fort Worth to the Diocese of Orange, in Orange, California, to succeed retiring Bishop Tod David Brown, 76. Vann was formally installed as the fourth bishop of the Diocese of Orange on December 10, 2012. Vann speaks Spanish and Vietnamese in addition to English.