Henry Moeller was born in Cincinnati, Ohio, to Bernard and Teresa (née Witte) Moeller, who were immigrants from Westphalia. He was the oldest of seven children; one of his sisters became a nun, and two brothers also became priests. His father worked as a cabinet maker and carpenter before becoming a bricklayer and building contractor. He was baptized by Father John Henry Luers the day after his birth, and received his early education at the parochial school of St. Joseph Church in the West End.
In 1863, Moeller entered St. Xavier College, from where he graduated with highest honors in 1869. He was then sent by Archbishop John Baptist Purcell to study philosophy and theology at the Pontifical North American College in Rome. In his competitive examinations, he won three first prizes in theology. He was ordained a subdeacon on November 2, 1875, and a deacon on the following November 10.
On June 10, 1876, Moeller was ordained to the priesthood by Archbishop Giulio Lenti at the Basilica of St. John Lateran. That same year he received his Doctor of Divinity degree from the Urban College of Propaganda. Following his return to Ohio, he was appointed pastor of St. Patrick Church in Bellefontaine in September 1876. He then served as a professor at Mount St. Mary's Seminary of the West in Norwood from 1877 to 1879.
In November 1879, Moeller was granted a leave of absence from the Archdiocese of Cincinnati to assist Bishop Silas Chatard of the Diocese of Vincennes in Indiana. He served as secretary to Bishop Chatard until 1880, when he was recalled to Cincinnati by Archbishop William Henry Elder to serve as his own secretary. He served as chancellor of the archdiocese from 1886 to 1900.
On April 6, 1900, Moeller was appointed the third Bishop of Columbus by Pope Leo XIII. He received his episcopal consecration on the following August 25 from Archbishop Elder, with Bishops Henry Richter and Thomas Byrne serving as co-consecrators, at St. Peter in Chains Cathedral in Cincinnati. He was installed at St. Joseph Cathedral in Columbus on August 27. During his brief tenure, he worked to eliminate the debt the diocese incurred from building the cathedral, established parish boundaries for Franklin County, and created three new parishes and four missions. In 1902, he presided over the fifth diocesan synod, which set regulations for the needs of the clergy and people of the diocese.
Moeller was named Coadjutor Archbishop of Cincinnati and Titular Archbishop of Areopolis on April 27, 1903. As coadjutor, he assumed the administrative duties of the archdiocese. Upon the death of Archbishop Elder, Moeller succeeded him to become the fourth Archbishop of Cincinnati on October 31, 1904. He was formally installed as archbishop and received the pallium on February 15, 1905. In 1921, he condemned several forms of dancing (including the Shimmy and Camel Walk) as well as bare female shoulders at social functions.
Moeller later died in Cincinnati at age 75. He is buried in the mausoleum at St. Joseph Cemetery in Price Hill.
Archbishop Moeller High School, a parochial school near Cincinnati, Ohio, was named for Bishop Moeller.