During his priestly ministry, he served as archdiocesan Assistant Superintendent of Schools and pastor of Holy Name Parish in Birmingham. From 1977 to 1985, he was rector of his alma mater of Sacred Heart Seminary. He later became director of the Department of Formation, and pastor of St. Rene Goupil Parish in Sterling Heights in 1984.
On November 23, 1993, Harrington was appointed Auxiliary Bishop of Detroit and Titular Bishop of Uzalis by Pope John Paul II. He received his episcopal consecration on January 6, 1994 from Archbishop Adam Maida, with Bishops Dale Melczek and Walter Schoenherr serving as co-consecrators. Harrington chose as his episcopal motto: "Have life more abundantly" (John 10:10). As an auxiliary to Maida, he served as Vicar of the Office of Pastoral Services for Parishes in the archdiocesan curia, Episcopal Liaison for the Pope John Paul II Cultural Center, and regional bishop for Macomb and St. Clair Counties.
He was later named the seventh Bishop of Winona, Minnesota, on November 4, 1998. He was formally installed as Winona's ordinary on the fifth anniversary of his episcopal consecration, January 6, 1999.
Within the United States Conference of Catholic Bishops, Bishop Harrington chaired the Committee on Education and sat on the Ad Hoc Committee on Catholic Bishops and Catholic Politicians In these offices, he has expressed his belief that Catholic politicans should oppose abortion. He is also a member of the Priestly Life and Ministry Committee and its liaison to the Subcommittee for Lay Ministry