Henry Moeller was born in Cincinnati on December 11, 1849, to Bernard and Theresa Witte Moeller, who were immigrants from Westphalia in Germany. Henry was the oldest of seven children. One of his sisters became a nun, and two brothers became priests as well.
Henry was educated at St. Joseph's parochial school, St. Xavier College in Cincinnati, and the American College in Rome, where he excelled at theology. He was ordained to the priesthood in St. John Lateran on June 10, 1876 by Archbishop Giulio Lenti of Nepi Sutri. Upon returning to America, Fr. Moeller served briefly in Bellefontaine, Ohio, then was a professor at Mt. St. Mary of the West Seminary in Norwood, Ohio.
In 1881, Fr. Moeller became secretary to Archbishop William Elder, and was named Chancellor of the Archdiocese of Cincinnati in 1886. On April 6, 1900, Fr. Moeller was appointed Bishop of Columbus. He was consecrated at St. Peter in Chains Cathedral, Cincinnati, that August 25 by Archbishop Elder. He came to Columbus and was installed in St. Joseph Cathedral on August 27.
Though the shortest episcopate in the history of the Diocese (just less than three years), Bishop Moeller is credited with setting Columbus on the right course for the newly-dawned 20th Century. He began the work of truly eradicating the large debt with which the Diocese was saddled as a result of its erection and the building of St. Joseph Cathedral. He also established parish boundaries for Franklin County, and erected three new parishes and four missions. In 1902 he convened the fifth synod of the Diocese to set regulations for questions pertaining to the needs of the clergy and people of the Diocese. In 1900 he consecrated Holy Name Church in Steubenville, which is now the cathedral church of that diocese.
On April 27, 1903, Bishop Moeller was appointed Titular Archbishop of Areopolis and coadjutor to Archbishop Elder. He left Columbus and arrived in Cincinnati on June 26. On Elder's death, he succeeded as fourth Ordinary of Cincinnati on October 31, 1904 and was installed in the Cathedral there on February 15, 1905.
Archbishop Moeller died January 5, 1925, and is interred in the mausoleum at St. Joseph Cemetery in the Cincinnati suburb of Pine Hill.