Joseph Benedict Reardon was born March 21, 1904, in Braddock, Pennsylvania, and received his elementary and secondary education at St. Thomas School in Braddock. After three years of study at Duquesne University in Pittsburgh, Pennsylvania, he entered the Dominican novitiate at St. Joseph Priory, Somerset, Ohio, and made profession there on August 25, 1923.

After taking philosophical studies at St. Rose Priory, Springfield, Kentucky, and at the House of Studies in River Forest, Illinois, Brother Innocent Reardon continued studies in theology at the House of Studies in Washington, D.C., where he was ordained to the priesthood on June 17, 1929. In 1930, he completed work for the Lectorate in theology from the House of Studies and for a master's degree in philosophy from Catholic University of America before being selected for two years' additional study at the Angelicum in Rome.

Father Reardon was first assigned to teach canon law on the theology faculty at St. Joseph Priory, Somerset, Ohio. In 1934, he was sent to River Forest, Illinois, to teach fundamental theology and church history in the Studium in addition to teaching philosophy courses at Rosary College and De Paul University and serving as chaplain for Trinity High School in River Forest. By 1938, he was named full-time professor of philosophy at De Paul University and continued to teach there until he volunteered for service as an Army chaplain in 1943. After his discharge from the Armed Forces in 1946, he returned to his faculty position at De Paul and his residence in River Forest.

In August 1947, Father Reardon moved to the new priory building at St. Pius V in Chicago. In January 1948, he was elected prior of the community and named pastor of St. Pius V Parish. When his term of office as prior and pastor ended in 1951, he taught for six months at Dominican College, Ursuline College, and Xavier University in New Orleans, Louisiana, before being assigned to St. Dominic's community in Denver as professor of theology and philosophy at Loretto Heights College.

In 1953, Father Reardon was named professor of theology and chaplain at St. Theresa's College in Winona, Minnesota. In 1963, he moved to New Orleans to teach at Xavier University until he was assigned to Houston, Texas, in 1968 to serve as chaplain and instructor at the Dominican Sisters' Motherhouse in Houston. In 1970, the chaplaincy at St. Dominic's Villa in Houston was added to his list of duties while he continued to teach special summer courses each year for the Dominican Sisters in Springfield, Illinois. In spite of suffering increasing cardiac difficulties, Father Reardon continued to serve the sisters at St. Dominic's Villa to the best of his ability until he died of heart failure on November 1, 1977. Following services at Holy Rosary Church. he was buried in the Dominican plot in Houston on November 4.