The second of seven children, Edward Slattery was born in Chicago, Illinois, to William Edward and Winifred Margaret (née Brennan) Slattery; both his paternal and maternal grandparents emigrated to the United States from Ireland. After attending Visitation of the BVM Grade School and Archbishop Quigley Preparatory Seminary, he studied at St. Mary of the Lake Seminary, from where he obtained Bachelor of Arts and Master of Divinity degrees.
Slattery was ordained to the priesthood by John Cardinal Cody on April 26, 1966, and then served as associate pastor of St. Jude the Apostle Parish in South Holland until 1971. During this time, he also earned a Master's degree from Loyola University. He was Vice-President (1971–76) and President (1976–94) of the Catholic Church Extension Society, a Chicago-based funding agency for the American home missions. While working at Extension, he was named associate pastor at the inner-city Hispanic parish of St. Rose of Lima on the south side of Chicago in 1973. He later served as pastor of St. Rose of Lima from 1976 to 1989.
Service as bishop
On November 11, 1993, Slattery was appointed the third Bishop of Tulsa, Oklahoma, by Pope John Paul II, who consecrated him on January 6, 1994, with Archbishops Giovanni Re and Josip Uhac serving as co-consecrators, in St. Peter's Basilica in Rome. He selected as his episcopal motto: "Tu Solus Sanctus", meaning, "You alone are the Holy One."
In 2006, Slattery said that if a law was passed criminalizing the act of aiding illegal immigrants "then [he] will become a criminal," adding, "When it becomes a crime to love the poor and serve their needs, then I will be the first to go to jail for this crime, and I pray that every priest and every deacon in this diocese will have the courage to walk with me into that prison." In 2007, he issued a 21-page pastoral letter  in which he condemned Oklahoma House Bill 1804, a strict anti-illegal immigration law which Slattery claimed creates "an atmosphere of repression and terror."
During the 2008 presidential election, Slattery criticized the Catholic House Speaker Nancy Pelosi and U.S. Senator Joe Biden for their remarks on abortion on Meet the Press, describing their positions as "clearly inconsistent with Catholic teaching" and "plainly false."
Slattery was a conservative on question of liturgical practice. He returned to the practice of celebrating the Eucharistic liturgy in this cathedral using the ancient style in which the priest and the congregation face the same direction, ad orientem. He believed this form had a number of advantages over the form of in which the priest faces the congregation. On April 24, 2010, he celebrated High Mass at the Basilica of the National Shrine of the Immaculate Conception to mark the fifth anniversary of Benedict XVI's papacy, wearing the rarely seen cappa magna.
On February 2, 2012, Bishop Slattery released a statement in response to the contraceptive mandates issued by the United States Department of Health and Human Services under the Patient Protection and Affordable Care Act. Slattery joined other bishops in the United States Conference of Catholic Bishops in opposing the mandate.