He was born on August 15, 1852 in Ireland, the son of Richard Harding. He emigrated in 1867 to the United States, settling in Brooklyn, Kings County, New York. He became a naturalized citizen in 1870 and spent several years a businessman.
He graduated from Trinity College, Hartford, Connecticut in 1879. He completed his studies at the Berkeley Divinity School, graduating in 1882.
He married in 1887 Justine Prindle Douglas, who was born on Jun. 16, 1853 in New York City and died on February 6, 1909 in Washington, D.C. She was the daughter of Dr. John Hancock Douglas, an 1843 graduate of Williams College, and the University of Pennsylvania School of Medicine in 1847. He was the personal physician for President Ulysses S. Grant, attending him from 22 October 1884, till the death of the latter, 23 July 1885. Alfred and Justine were the parents of four children, three of whom survived to adulthood: Alfred J., Charlotte G. and Paul Curtis. A son, Douglas died in 1891 at the age of 3.
In 1882, he was ordained a deacon by Abram N. Littlejohn, the first Episcopal Bishop of Long Island and in 1883 he was ordained a priest again by Bishop Littlejohn. The year of his deaconate was spent as an assistant to the Rev. Henry M. Nelson, Jr., rector of Trinity Church, Geneva, New York. From 1883 to 1887, he was the assistant rector of Old St. Paul's Parish in Baltimore, Maryland. He was third rector of St. Paul's, K Street, Washington, D.C. serving from 1887 until 1909 when he became the Bishop of Washington, D.C. This parish has given special attention to music, it being the first in the city to introduce the choral service. In 1889 he received the call to Christ Church Cathedral, St. Louis, Missouri, but declined.
On January 25, 1896 he was consecrated the second Episcopal Bishop of Washington at Trinity Episcopal Church in Washington, D.C. The consecrator was Bishop Charles Edward Woodcock, the third Episcopal Bishop of Kentucky. Alfred Harding was the 240th bishop consecrated in the Episcopal Church.
When the Harriet Lane Johnston choir school (St. Albans) opened, nine years after the National Cathedral School for Girls, Harding made Edgar Priest supervisor of music at these schools in August 1909. His formal appointment as the Cathedral’s first organist and choirmaster came in 1911 in anticipation of the opening of Bethlehem Chapel for services the following May.
He died on May 2, 1923 in Washington, D.C. Both he and his wife are buried in the Resurrection Chapel of Washington National Cathedral.